Question

5(2x)=5/16 what would x be in this logarithmic equation?

Answer 1

The required value of x in the given logarithmic equation is -0.36

Explanation:

The given logarithmic equation is :

`5^(2x)=(5)/(16)`

We need to find the required value of x in the given logarithmic equation.

`5^(2x)=(5)/(16)\\\\\text{Taking log on both the sides}\\\\\log 5^(2x)=\log((5)/(16))\\\\\implies 2x=(\log 5-\log 16)/(\log 5)\\\\\implies 2x=(0.699-1.204)/(0.699)\\\\\implies 2x = (-0.505)/(0.699)\\\\\implies 2x = -0.72\\\\\implies x = -0.36`

Hence, the value of x in the given logarithmic equation is -0.36