Solve the exponential equation (3/5)^x=7^(1-x) without using a calculator?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The equation `(3/5)^x=7^(1-x)` has to be solved.

`(3/5)^x=7^(1-x)`

Use the formula `a^(b - c) = a^b/a^c`

=> `(3/5)^x = 7/7^x`

Use the formula `a^x*b^x = (a*b)^x`

=> `((3*7)/5)^x = 7`

=> `(21/5)^x = 7`

To solve further take the logarithm of both the sides.

`log((21/5)^x) = log 7`

Use the formula `log a^x = x*log a`

=> `x*log(21/5) = log 7`

=> `x = (log 7)/(log(21/5))`

The solution of the equation `(3/5)^x=7^(1-x)` is `x = (log 7)/(log(21/5))`

Approved by eNotes Editorial Team