Question

Solve each exponential equation.
32^x = 81

Answer 1

The solution is
`x = 1.268`.

Explanation:

The best way to solve this exponential equation is applying the logarithm of base 10 to each side of the equality.

It is also important to remember the following logarithm proprierty:

`\log{a^(b)} = b \log{a}`

So

`32^(x) = 81`

`\log{32^(x)} = \log{81}`

`x\log{32} = \log81`

`1.505x = 1.908`

`x = (1.908)/(1.505)`

`x = 1.268`

The solution is
`x = 1.268`.