Question

How do you solve `3^(2x) = 81`?

Answer 1

The unique solution is `x = ln(81)/(2ln(3))`.

Explanation:

This is an equation with the x at the power, so you have to write `3^(2x)` as an exponential (I assume x is a real number) since every real power function is in fact an exponential, hence the new equation : `exp(2xln(3)) = 81.`

You can now apply the natural logarithm at both sides of the equation (ln is a strictly growing function on R, which guanrantees you that the x you will find is unique) : `2xln(3) = ln(81)`.

Now you can divide on both sides by `2ln(3)`, and voilà!