Question

How do you solve `7^(2x-3) - 4 = 14`?

Answer 1

You must work with the fact that `a^n = m -> loga^n = logm`

Explanation:

`7^(2x - 3) = 18`

`log7^(2x - 3) = log18`

Simplify using the rule `loga^n = nloga`

`(2x - 3)log7 = log18`

`2xlog7 - 3log7 = log18`

`2xlog7 = log18 + 3log7`

Use the rule `log_an + log_am = log_a(n xx m)`

`x(2log7) = log(18 xx 343)`

`x = log6174/log49`

`x = 2.24`

Make sure to ask your teacher whether or not they require your answer in logarithmic (exact) form.

Hopefully this helps!