Question

solve 3 to the power x=5 to the power x-2

Answer 1

Hello friend!


3^x = 5^(x-2)

Applying log on both the sides

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

【log n^a = a log n】

x log 3 = (x-2) log 5

x log 3 = x log 5 - 2log 5

2log 5 = x log 5 - x log 3

Taking x common

2 log 5 = x ( log 5-3)

2 log 5 / log 2 = x

【 x log n = log n ^ x】

log 5^2 / log 2 = x

log 25 / log 2 = x

Hope it helps!

Answer 2

Answer:

Step-by-step explanation:

3^x=5^x-2

Apply log on both sides

Iog3^x=log5^x-2

We know that loga^n = n log a

So,

X log 3= x-2 (log 5)

X log 3 =X (log 5) -2 (log 5)

X log 3 = X log 5 - 2 log 5

X log 3 - X log 5 = -2 log 5

-(X log 3 -X log 5) = 2 log 5

-X log 3 + X log 5 = 2 log 5

X(log 5-log 3) = 2log 5

Again,

Log a- log b=log a÷b

So,

X ( log 5/3)= 2 log 5

X (log 5/3)= log5^2

X (log 5/3) = log 25

X = log 25/log 5/3

That's it

Please mark as brainliest