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

1 Answer

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!