Question

How do you solve `5^(x-7) = 4`?

Answer 1

You must convert to logarithmic form and solve for x.

Explanation:

`5^(x - 7) = log4`

Simplify using the rule `log_nx^a = alog_nx`

`(x - 7)log5 = log4`

`xlog5 - 7log5 = log4`

`x(log5 - 7log5) = log4`

#x = log4/(log5 - log5^7)

Using the rule `log_am - log_an = log_a(m / n)`

`x = log4/log(5/78125)`

Using the rule `loga/logb = log_ba`:

`x = log_(1/(15 625))4`

Ask your teacher what they require when it comes to the answer. Some teachers like the answer rounded to a certain number of decimals, while some want the exact value answer.

Practice exercises:

1. Solve for x.

a) `2^(x + 4) = 5`

b) `3^(2x - 7) = 2^(x + 1)`

c) `4 xx 2^(x + 2) = 3^(3x - 4)`

Good luck!