Question

How do you solve `5*11^(5a+10)=57`?

Answer 1

`a=-1.797`

Explanation:

`5 * 11^(5a+10)=57`

`(5*11^(5a+10))/5=57/5color(white)(aaa)`Divide both sides by 5

`11^(5a+10)=57/5`

`log(11^(5a+10))=log (57/5)color(white)(aaa)`Take the log of both sides

`(5a+10)log11=log(57/5)color(white)(aa)`Use the log rule `logx^a=alogx`

`frac{(5a+10)log11}{log11}=frac{log(57/5)}{log11}color(white)(aa)`Divide both sides by log11

`5a+10=frac{log(57/5)}{log11}`

`color(white)(aa)-10color(white)(aaa)-10color(white)(aaa)`Subtract 10 from both sides

`5a=frac{log(57/5)}{log11}-10`

`(5a)/5=frac{frac{log(57/5)}{log11}-10}{5}color(white)(aaa)`Divide both sides by 5

`a=-1.797color(white)(aaa)`Use a calculator