Question

Without using log, Solve for x.


`25^(2x+3) =125^(2)`

Answer 1

x=2.5

as

25squredx+3 so u take the power 3 to the other side then it will be

25squredx =125 to the power -1

squredx=125÷25

x=5÷2

x=2.5

Answer 2

Answer:
`x=-6`

Explanation:

Remember that:

`a^x=a^y`→
`x=y`

The Power of a power property states that:

`(a^m)^n=a^(mn)`

Then, descompose 25 and 125 into their prime factors:

`25=5*5=5^2\\125=5*5*5=5^3`

Rewrite the expression:

`(5^2)^(2x+3) =(5^3)^(x)`

Then:

`5^(4x+6) =5^(3x)\\4x+6=3x`

Now, you can solve for x. Therefore you get that the result is

`4x+6=3x\\4x-3x=-6\\x=-6`