Question

Solve log 49[(log:(5x – 2)] =​

Answer 1

Answer:

5x-3 y53 1/36-79/619-748+930571

Answer 2

Answer:

The value of $x$ is $26$

Step-by-step explanation:

Given $log_{49} [log_{2} (5x-2)]=\frac{1}{2}$

We have to find the value of $x$

We know that the formula is

$log_{a} y=b\\a^{b} =y$

Logarithm as inverse function of exponential function

The logarithmic function

$b=log_{a} y$

is the inverse function of the exponential function,

$y=a^{b}$

$log_{49}[log_{2}(5x-2)]=\frac{1}{2}$

Using

$log_{a} y=b\\a^{b} =y$

where

$a=49\\b=1/2\\y=log_{2}(5x-2)$

Substitute these values in above formula

$1/2$ power is equivalent to square root

$\sqrt{49} =log_{2}(5x-2) \\7=log_{2} (5x-2)\\log_{2}(5x-2)=7$

Again using

$log_{a}y=b\\ a^{b} =y$

where

$a=2\\b=7\\y=(5x-2)$

substitute these values in the above formula

$2^{7} =5x-2\\128=5x-2\\130=5x\\x=26$