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

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Top Answer

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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


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))`

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aruv | High School Teacher | (Level 2) Valedictorian

Posted on

Solve the exponential equation (3/5)^x=7^(1-x).


Taking log both sides







In above we have used the following rules in logarithm.

`1. log(x/y)=logx-logy`

`2. logx^m=mlogx`