Question

Solve:

3^(2x+1)=12

Show your workings:

Answer 1

3^(2x+1) = 12

We can rewrite this as:
3^(2x) * 3^(1) = 12
(3^2)^x = 12/3
9^x = 4

Get the natural logarithm of both sides:
ln (9^x) = ln (4)
x * ln(9) = ln(4)
x = ln(4) / ln(9)

We can further simplify this as:
x = ln(2^2) / ln(3^2)
x = 2*ln(2) / [2*ln(3)]
x = ln(2) / ln(3)

Hope this helps~ `u`

Answer 2

take logs of both sides

log 3^(2x+1) = log 12
(2x+1)log3 = log12
2x+1 = log12/log3
2x = log12/log3 - 1
x = (log12/log3 - 1)/2
= .....