How do you solve 3^(2x+1) = 5?

1 Answer
Aug 3, 2017

x = 0.232 (to 3 sf)

Explanation:

We will not attempt to treat this as an exponential equation by working with the bases, because 5 is not a power of 3.

Find the log of both sides.

log 3^(2x+1) = log5" "larr use the log power law

(2x+1) log3 = log5" "larr isolate the x term

2x+1= log5/log3

2x = log5/log3-1

x = (log5/log3-1)div2

There are no laws to simplify this, so use a calculator to find a value for x

x = 0.23248676