Question

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

Answer 1

Step-by-step explanation:

Given : Expression 3^x = 5^{x-2}3

x

=5

x−2

To find : Solve the expression ?

Solution :

3^x = 5^{x-2}3

x

=5

x−2

Taking log both the sides,

\log 3^x = \log 5^{x-2}log3

x

=log5

x−2

Applying logarithmic property, \log n^a = a \log nlogn

a

=alogn

x \log 3 = (x-2) \log 5xlog3=(x−2)log5

x \log 3 = x \log 5 - 2\log 5xlog3=xlog5−2log5

2\log 5 = x \log 5 - x \log 32log5=xlog5−xlog3

2 \log 5 = x (\log 5 - \log 3)2log5=x(log5−log3)

x=\frac{2 \log 5}{\log 5 - \log 3}x=

log5−log3

2log5

x=6.30x=6.30

Therefore, the value of x is 6.30.