Question

Find the exact solution of the equation. 7^x = 8

A. x = In7 / In8
B. x = 7 / 8
C. x = In(8 / 7)
D. x = (In8 / In7)

Answer 1

`x = ((ln8))/((ln7))`

Explanation:

Solve for x

Take the logarithm of both sides of the equation to remove the variable from the exponent. We have:

`ln(7x) = ln(8)`

Expand

`ln(7)`

by moving x outside the logarithm. It becomes:

`x \: ln(7) = ln(8)`

Divide each term in

`x \: ln(7) = ln(8) \: by \: ln(7)`We have:

`(x \: ln(7))/(ln(7)) = (ln(8))/(ln(7))`

:. Exact form:

`(ln(8))/(ln(7))`