Question

logx/log5=log9/log1/3

Answer 1

i hope this will usful to u

Answer 2

Answer:

The value of x is 0.04.    

Step-by-step explanation:

Given : Expression $\frac{\log x}{\log 5}=\frac{\log 9}{\log \frac{1}{3}}$

To find : Solve for x?

Solution :

Expression $\frac{\log x}{\log 5}=\frac{\log 9}{\log \frac{1}{3}}$

$\frac{\log x}{\log 5}=\frac{\log 3^2}{\log 3^{-1}}$

Apply logarithmic property,

$\log a^x=x\log a$

$\frac{\log x}{\log 5}=\frac{2\log 3}{-1\log 3}$

Cancel $\log 3$

$\frac{\log x}{\log 5}=-2$

Applying logarithmic property, $\frac{\log a}{\log b}=\log_b a$

$\log_5 x=-2$

Again using logarithmic property,

$\log_b a=x\\\Rightarrow a=x^b$

$x=5^{-2}$

$x=\frac{1}{5^2}$

$x=\frac{1}{25}$

$x=0.04$

Therefore, The value of x is 0.04.