Question

use a definição para calcular:
log5/3 0,6

Answer 1

Pela definição:

$\large\fbox{ \ell og_{a}(b)=y~\Leftrightarrow~a^y=b }~~~~(0\ \textless \ a \neq 1)$

Então...

$\large\begin{array}{l}\ell og_{\frac{5}{3}}(0,6)~\Leftrightarrow~\begin{pmatrix}\dfrac{5}{3}\end{pmatrix}^y=0,6\\\\\\\begin{pmatrix}\dfrac{5}{3}\end{pmatrix}^y=\dfrac{6}{10}\\\\\\\begin{pmatrix}\dfrac{5}{3}\end{pmatrix}^y=\dfrac{3}{5}\\\\\\\begin{pmatrix}\dfrac{5}{3}\end{pmatrix}^y=\begin{pmatrix}\dfrac{5}{3}\end{pmatrix}^{-1}\end{array}$

Lembrando que

$\large\fbox{ a^b=a^c~\Longleftrightarrow~b=c }~~~~(0\ \textless \ a \neq 1)$

$\large\begin{array}{l}\begin{pmatrix}\dfrac{5}{3}\end{pmatrix}^y=\begin{pmatrix}\dfrac{5}{3}\end{pmatrix}^{-1}\\\\\\\fbox{ y=-1 }\\\\\\\therefore~\large\fbox{ \ell og_{\frac{5}{3}}(0,6)=-1 }\end{array}$

Answer 2

Resposta:

$Log_{\frac{5}{3}}}0,6=\bf{-1}$

Explicação passo-a-passo:

$Log_{a} b=x\:\text{sendo}\:a^{x} =b$

ₐ = Base

b = Logaritmando

x = Logaritmo

Resolução:

$Log_{\frac{5}{3}} 0,6=x$

ₐ = 5/3

b = 0,6

x = ? (chamaremos de x)

$a^{x} =b\\(\frac{5}{3})^{x} =0,6\\\\\diagup\!\!\!\!(\frac{5}{3})^{x}=\diagup\!\!\!\!(\frac{5}{3})^{-1}\\\\\bf{x=-1}$