Question

If
3 power x =5 power x-2
then find the value of x?​

Answer 1

Step-by-step explanation:

3^x = 5^(x-2)

we need to take log to solve this.

taking log both side

log 3^x = log 5^(x-2)

xlog3 = (x-2)log5

xlog3 = xlog5 - 2log5

xlog5 - xlog3 = 2log5

x(log5 - log3) = 2log5

x log(5/3) = 2log5

x = 2log5/log(5/3)

x= 2log(5-5/3)

x = 2 log10/3

x = 2(log10-log3)