Assinale a falsa:
a)
$\phantom{X}log_{\,2\,}8\,=\,3\phantom{X}$
b)
$\phantom{X}log_{\,4\,}16\,=\,2\phantom{X}$
c)
$\phantom{X}log_{\,3\,}9\,=\,2\phantom{X}$
d)
$\phantom{X}log_{\,10\,}100\,=\,10\phantom{X}$
e)
$\phantom{X}log_{\,10\,}1000\,=\,3\phantom{X}$
✓ mostrar resposta ... O logaritmo
de 3 na base 81 vale:
✓ mostrar resposta ... O valor de $\,log_{\,100\,}0,001\,$ é:
✓ mostrar resposta ... Calcular o logaritmo de $\phantom{X}8\centerdot \sqrt[\LARGE 3\,]{\,2\,}\phantom{X}$ na base $\phantom{X}2\centerdot\sqrt{2}\,$
✓ mostrar resposta ... Determinar a base de um sistema de logaritmos em que o logaritmo
de 81 vale 2 .
✓ mostrar resposta ... (UnB) Se $\,a\,=\,log_{\,8\,}225\,$ e $\,b\,=\,log_{\,2\,}15\,$ então:
a)
$\,a\,=\,\dfrac{2b}{3}\,$
b)
$\,a\,=\,\dfrac{b}{2}\,$
c)
$\,a\,=\,\dfrac{3b}{2}\,$
d)
$\,a\,=\,\dfrac{b}{3}\,$
e)
$\,a\,=\,\dfrac{2b}{5}\,$
✓ mostrar resposta ... (VUNESP) O valor da expressão $\phantom{X}\dfrac{\;log_{\,3\,}9\,-\,(-3)^{\large 2}\,-\,\sqrt[\Large 3\,]{-27}\;}{\;(-1)^{\large 3}\,-\,(-\,\dfrac{1}{2})^{\large 2}\,-\,\dfrac{11}{4}\;}\phantom{X}$ é:
c)
$\,\dfrac{7}{2}\phantom{XX}$
✓ mostrar resposta ... (PUCC) O logaritmo de um número
x na base
a é
-1 , e o logaritmo do mesmo número
x na base
2a é
-2 . Então a
soma a + x é: a)
$\,\dfrac{3}{\,4\,}\,$
b)
$\,4\,$
c)
$\,16\,$
d)
$\,\dfrac{1}{\,4\,}\,$
e)
$\,\dfrac{17}{\,4\,}\,$
✓ mostrar resposta ... O valor de $\phantom{X}{\Large 9\,}^{\Large log_{{}_{\,3\,}}\sqrt{\LARGE\,2\,} }\phantom{X}$ é:
a)
$\,\sqrt{\,2\,}\,$
b)
$\,2\,$
c)
$\,9\,$
d)
$\,2^{\Large 9}\,$
e)
$\,(\sqrt{\,2\,})^{\Large 9}\,$
✓ mostrar resposta ... Sendo$\phantom{X}{\large e}\phantom{X}$o número de Neper, o valor de $\phantom{X}{\Large e\,}^{{}^{\LARGE 1\,+\,log_{\Large \,e\,}\pi}}\phantom{X}$ é:
c)
$\,\frac{\,\pi\,}{e}\,$
d)
$\,\frac{\,e\,}{\pi}\,$
✓ mostrar resposta ... Sendo $\phantom{X}log_{{}_{\Large\,5\,}}a\;=\;m\phantom{X}$ e $\phantom{X}log_{{}_{\Large\,5\,}}b\;=\;n\phantom{X}$
com a > 0 e b > 0 , calcular, em função
de m e n , o valor dos logaritmos apresentados a seguir:
b)
$\,log_{\,5\,}(\dfrac{a}{b})\,$
c)
$\,log_{\,5\,}(a^2\,\centerdot\,b^3)\,$
d)
$\,log_{\,5\,}(\sqrt[\Large 3\,]{a}\,\centerdot\,\sqrt[\Large 4\,]{b})\,$
✓ mostrar resposta ... resposta:
a)m + n b) m - n c) 2m + 3n d)$\,\dfrac{1}{3}m\,+\,\dfrac{1}{4}n\,$ × (PUC) Para
todo x > 0 , $\,log_{{}_{\Large \,2\,}}4x\,$ é igual a:
a)
$\,2\,+\,log_{\,2\,}x\,$
b)
$\,2\,log_{\,2\,}x\,$
c)
$\,4\,log_{\,2\,}x\,$
d)
$\,log_{\,8\,}x\,$
e)
$\,log_{\,2\,}(4\,+\,x)\,$
✓ mostrar resposta ... (MACKENZIE) O valor de $\phantom{X}log_{{}_{\Large\,3\,}}5\,\centerdot\,log_{{}_{\Large\,25\,}}27\phantom{X}$ é:
✓ mostrar resposta ... (FGV) O produto $\;(log_{{}_{\Large \,3\,}}2)\,\centerdot\,(log_{{}_{\Large \,2\,}}5)\,\centerdot\,(log_{{}_{\Large \,5\,}}3)\;$ é igual a:
✓ mostrar resposta ... Supondo satisfeitas todas as condições de existência e sabendo-se que $\phantom{X}log_{{}_{\LARGE\,c\,}}a\,=\,\dfrac{1}{3}\phantom{X}$ e $\phantom{X}log_{{}_{\LARGE\,c\,}}b\,=\,20\;$, o valor de $\phantom{X}log_{{}_{\LARGE\,c\,}}(\dfrac{\;a^{{}^{\Large 3}}\,\sqrt[\Large 4]{\,b\,}\;}{c^{\,\large 2}})\phantom{X}$ é:
✓ mostrar resposta ... (PUCC) A expressão $\phantom{X}log _2\,\sqrt[\large 210\,]{2}\,+\,log _2\,\sqrt[\large 210\,]{2^2}\,+\,...\,+\,log _2\,\sqrt[\large 210\,]{2^{20}}\phantom{X}$ é igual a:
a)
2
b)
$\,\dfrac{1}{\,\sqrt{210\,}}\,$
c)
$\,\dfrac{1}{\,210\,}\,$
d)
0
✓ mostrar resposta ... Assinale a falsa:
a)
$\,colog_{\,3\,}81\,=\,-4\,$
b)
$\,colog_{\,2\,}16\,=\,-4\,$
c)
$\,antilog_{\,2\,}3\,=\,8\,$
d)
$\,antilog_{\,3\,}4\,=\,81\,$
e)
$\,colog_{\,3\,}27\,=\,3\,$
✓ mostrar resposta ... Calcular os seguintes logaritmos:
a)
$\,log_{{}_{\Large \,2\,}}\dfrac{1}{8}\,$
b)
$\,log_{{}_{\Large \,8\,}}4\,$
c)
$\,log_{{}_{\Large \,0,25\,}}32\,$
✓ mostrar resposta ... resposta:
a) -3 b) 2/3 c) -5/2 × Calcular os seguintes logaritmos:
a)
$\,log_{{}_{\Large \,4\,}}16\,$
b)
$\,log_{{}_{\Large \,3\,}}\dfrac{1}{9}\,$
c)
$\,log_{{}_{\Large \,81\,}}3\,$
d)
$\,log_{{}_{\Large \,\frac{1}{2}\,}}8\,$
e)
$\,log_{{}_{\Large \,7\,}}\dfrac{1}{7}\,$
f)
$\,log_{{}_{\Large \,27\,}}81\,$
g)
$\,log_{{}_{\Large \,125\,}}25\,$
h)
$\,log_{{}_{\Large \,\frac{1}{4}\,}}32\,$
i)
$\,log_{{}_{\Large \,9\,}}\dfrac{1}{27}\,$
j)
$\,log_{{}_{\Large \,0,25\,}}8\,$
k)
$\,log_{{}_{\Large \,25\,}}0,008\,$
l)
$\,log_{{}_{\Large \,0,01\,}}0,001\,$
✓ mostrar resposta ... resposta:
a) 2 b) -2 c) 1/4 d) -3 e) -1 f) 4/3 g) 2/3 h) -5/2 i) -3/2 j) -3/2 k) -3/2 l) 3/2 × Calcular, de acordo com a definição, os logaritmos:
a)
$\,log_{{}_{\Large \,2\,}}\sqrt{\,2\,}\,$
b)
$\,log_{{}_{\Large \,\sqrt[\Large 3\,]{7}\,}}49\,$
c)
$\,log_{{}_{\Large \,100\,}}\sqrt[\Large 3\,]{\,10\,}\,$
d)
$\,log_{{}_{\Large \,\sqrt{\,8\,}\,}}\sqrt{\,32\,}\,$
e)
$\,log_{{}_{\Large \,\sqrt[\Large 3\,]{\,5\,}\,}}\sqrt[\LARGE 4\,]{\Large\,5\,}\,$
f)
$\,log_{{}_{\Large \,\sqrt{27}\,}}\sqrt[\Large 3\,]{\,9\,}\,$
g)
$\,log_{{}_{\Large \,\frac{1}{\,\sqrt{\,3\,}\,}\,}}\sqrt{\,27\,}\,$
h)
$\,log_{{}_{\Large \,\sqrt[\Large 3\,]{\,4\,}\,}}\dfrac{1}{\,\sqrt{\,8\,}\,}\,$
i)
$\,log_{{}_{\Large \,\sqrt[\Large 4\,]{\,3\,}\,}}\dfrac{3}{\sqrt[\Large 3\,]{\,3\,}}\,$
✓ mostrar resposta ... resposta:
a) 1/2 b) 6 c) 1/6 d) 5/3 e) 3/4 f) 4/9 g) -3 h) -9/4 i) 8/3 j) -3/2 k) -3/2 l) 3/2 × Sendo
a , b e c números reais positivos, desenvolver as expressões abaixo.
a)
$\;log_{{}_{\Large \,2\,}}\left(\dfrac{\,2ab\,}{c}\right)\,$
b)
$\;log_{{}_{\Large \,3\,}}\left(\dfrac{\,a^{\large 3}b^{\large 2}\,}{c^{\large 4}}\right)\,$
c)
$\;log\,\left(\dfrac{\,a^{\large 3}\,}{\,b^{{}^{\Large 2}}\,\centerdot\,\sqrt{\,c\,}\,}\right)\,$
✓ mostrar resposta ... resposta:
a) $1\,+\,log_2\,a\,+\,log_2\,b\,-\,log_2\,c$ b) $3\,log_3\,a\,+\,2\,log_3\,b\,-\,4\,log_3\,c$ c) $\,3\,log\,a\,-\,2\,log\,b\,-\,\dfrac{1}{2}\,log\,c$ × Desenvolver as expressões abaixo aplicando as propriedades dos logaritmos.
a)
$\;log_{{}_{\Large \,5\,}}(\dfrac{\,5a\,}{bc})\,$
b)
$\;log_{{}_{\Large \,3\,}}(\dfrac{\,ab^2\,}{c})\,$
c)
$\;log_{{}_{\Large \,2\,}}\left(\dfrac{\,a^2\,\sqrt{\,b\,}\,}{\sqrt[\large \,3\,]{\,c\,}} \right) $
d)
$\;log_{{}_{\Large \,3\,}}\left(\dfrac{\,a\,\centerdot\,b^3\,}{c\,\centerdot\,\sqrt[\large \,3\,]{\,a^2\,}}\right)\,$
e)
$\;log\sqrt{\dfrac{\,ab^3\,}{c^2}}\,$
f)
$\;log_{{}_{\Large \,3\,}}\sqrt[\Large 3\,]{\dfrac{\,a\,}{\,b^2\,\centerdot\,\sqrt{\,c\,}}}\,$
g)
$\;log_{{}_{\Large \,2\,}}\sqrt{\dfrac{\,4a\,\sqrt{\,ab\,}}{\,b\;\sqrt[\Large 3\,]{\,a^2b\,}}}\,$
h)
$\;log\,\left(\sqrt[\LARGE 3\,]{\dfrac{\,a^{\large 4}\,\sqrt{\,ab\,}}{\,b^2\;\sqrt[\Large 3\,]{\,bc\,}}}\right)^{\Large 2}\,$
✓ mostrar resposta ... resposta:
a) $\,1\,+\,log_5a\,-\,log_5b\,-log_5c\,$ b) $\,log_3a\,+\,2\,log_3b\,-\,log_3c\,$ c) $2\,log_2a\,+\,\frac{1}{2}log_2b\,-\,\frac{1}{3}log_2c$ d) $\,\frac{1}{3}\,log_3a\,+\,3\,log_3b\,-\,log_3c$ e) $\frac{1}{2}\,log\,a\,+\,\frac{3}{2}log\,b\,-\,log\,c$ f) $\frac{1}{3}\,log\,a\,-\,\frac{2}{3}log\,b\,-\,\frac{1}{6}log\,c$ g) $\,2\,+\,\frac{5}{12}log_2a\,-\,\frac{5}{12}log_2b\,$ h) $\,3\,log\,a\,-\,\frac{11}{9}log\,b\,-\,\frac{2}{9}log\,c\,$ × Calcular:
a) $\,antilog_{\,2\,}(log_2\,3)\;$ b)$\,antilog_{\,3\,}(log_3\,5)\,$
✓ mostrar resposta ... Desenvolver aplicando as propriedades dos logaritmos
. Obs. a > b > c > 0 . a)
$\;log_{{}_{\Large \,2\,}}\dfrac{2a}{\;a^2\,-\,b^2\;}\;$
b)
$\;log_{{}_{\Large \,2\,}}\dfrac{a^2\,\sqrt{\,bc\,}}{\;\sqrt[\LARGE 5]{\,(a\,+\,b)^3}\;}\;$
c)
$\;log\left(c\,\centerdot\,\sqrt[\LARGE 3]{\dfrac{\;a(a\,+\,b)^2}{\sqrt{\;b\;}}} \right)\;$
d)
$\;log\left(\dfrac{\;\sqrt[\Large 5]{a(a\,-\,b)^2}\;}{\sqrt{a^2\,+\,b^2}} \right)\;$
✓ mostrar resposta ... Sendo a, b e c reais positivos, escreva as expressões cujos desenvolvimentos logaritmicos são dados.
a)
$\;log_{{}_{\Large \,2\,}}a\,+\,log_{{}_{\Large \,2\,}}b\,-\,log_{{}_{\Large \,2\,}}c\;$
b)
$\;2\,log\,a\;-\;log\,b\;-\;3\,log\,c\;$
c)
$\;2\,-\,log_{{}_{\Large \,3\,}}a\,+\,3\,log_{{}_{\Large \,3\,}}b\,-\,2\,log_{{}_{\Large \,3\,}}c\;$
d)
$\;\dfrac{\;1\;}{2}\,log\;a\,-\;2\,log\,b\;-\;\dfrac{\;1\;}{3}\,log\,c\;$
e)
$\;\dfrac{\;1\;}{3}\,log\;a\,-\;\dfrac{\;1\;}{2}\,log\,c\;-\;\dfrac{\;3\;}{2}\,log\,b\;$
f)
$\;2\;+\;\dfrac{\;\,1\,\;}{3}\,log_{{}_{\Large \,2\,}}a\,+\,\dfrac{\;\,1\,\;}{6}\,log_{{}_{\Large \,2\,}}b\,-\,log_{{}_{\Large \,2\,}}c\;$
g)
$\;\dfrac{\;1\;}{4}(log\,a\;-\;3\,log\,b\;-\;2\,log\,c)\;$
✓ mostrar resposta ... Se $\;log\,2\;=\;a\phantom{X}$ e $\phantom{X}log\,3\;=\;b\;$, colocar em função de $\,a\,$ e $\,b\,$ os seguintes logaritmos decimais:
d)
$\,log\,\sqrt{\,2\,}\,$
✓ mostrar resposta ... Sabendo que $\;log_{{}_{\Large \,30\,}}3\;=\;a\phantom{X}$ e $\phantom{X}log_{{}_{\Large \,30\,}}5\;=\;b\;$, calcular $\;log_{{}_{\Large \,10\,}}2\;$
✓ mostrar resposta ... resposta: $\,\frac{\;1\,-\,a\,-\,b\;}{1\,-\,1}\,$
× Sabendo que $\;log_{{}_{\Large \,20\,}}2\;=\;a\phantom{X}$ e $\phantom{X}log_{{}_{\Large \,20\,}}3\;=\;b\;$, calcular $\phantom{X}log_{{}_{\Large \,6\,}}5\phantom{X}$
✓ mostrar resposta ... resposta: $\,\frac{\;1\,-\,2a\;}{a\,+\,b}\,$
× Se $\;log_{{}_{\Large \,ab\,}}a\;=\;4\phantom{X}$, calcule $\phantom{X}log_{{}_{\Large \,ab\,}}\dfrac{\,\sqrt[\Large 3]{\;a\;}\,}{\,\sqrt{\;b\;}\,}\;$.
✓ mostrar resposta ... Se $\;log_{{}_{\Large \,12\,}}27\;=\;a\phantom{X}$, calcule $\phantom{X}log_{{}_{\Large \,6\,}}16\;$.
✓ mostrar resposta ... resposta: $\,\frac{4(3\,-\,a)}{a\,+\,3}\,$
× Calcular $\;A\,=\,log_{{}_{\Large \,3\,}}5\,\centerdot\,log_{{}_{\Large \,4\,}}27\,\centerdot\,log_{{}_{\Large \,25\,}}\sqrt{2}\;$.
✓ mostrar resposta ... Simplificar a expressão $\;a^{\large log_{{}_{\Large \,a}}b\;\centerdot\;log_{{}_{\Large \,b}}c\;\centerdot\;log_{{}_{\Large \,c}}d}\;$.
✓ mostrar resposta ... Simplificar a expressão $\phantom{X}{\Large a}^{{}^{\dfrac{\,log(log{\large\;a})\,}{log{\large\,a}}}}\;$
✓ mostrar resposta ... 