Question

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

Answer 1

Answer:

$x = \frac{(ln8)}{(ln7)}$

Step-by-step 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:

$\frac{x \: ln(7)}{ln(7)} = \frac{ln(8)}{ln(7)}$

:. Exact form:

$\frac{ln(8)}{ln(7)}$