Question

How do you solve the exponential equation `10^(x-3)=100^(4x-5)`?

Answer 1

`x=1`

Explanation:

Express the exponential on the right side with a `color(blue)"base of 10"`

`rArr10^(x-3)=(10^2)^(4x-5)`

`rArr10^(x-3)=10^(8x-10)`

Since the bases on both sides are 10 then equate the exponents.

`rArr8x-10=x-3`

`rArr7x=7`

`rArrx=1" is the solution"`