Question

How do you solve `4 ^(2x) = 6`?

Answer 1

You must use logarithms to solve.

Explanation:

If `a^n = b`, then `loga^n = logb`.

`log4^(2x) = log6`

Use the log rule `loga^n = nloga` to simplify further.

`2xlog4 = log6`

`x(log4^2) = log6`

`x = (log6)/(log16)`

`x = 0.65`

Make sure to ask your teacher if they want your answer in exact form (`x = (log6)/(log16)`) or rounded off to an x number of decimal points. I know that my teacher asks for two decimals after the point (`x = 0.65`), but some ask for 1, 3 or 0.

Practice exercises:

1. Solve for x:

`a) 2^(3x - 2) = 17`

`b) 3^(4x + 1) = 6^(3x - 3)`

Challenge problem:

Solve for x in `2^(2x - 3) + 5 = 3^(3x)`

Hint: think of the log addition rule.

Good luck!