Question

25^(2x+3) = 125^(2x+8)
please help and show work!!!!!!!

Answer 1

Let's solve up

`\\ \rm\rightarrowtail 25^(2x+3)=125^(2x+8)`

`\\ \rm\rightarrowtail 5^(2(2x+3))=5^(3(2x+8))`

`\\ \rm\rightarrowtail 5^(4x+6)=5^(6x+24)`

`\\ \rm\rightarrowtail 4x+6=6x+24`

`\\ \rm\rightarrowtail -18=2x`

`\\ \rm\rightarrowtail x=-9`

Answer 2

`x = -9`

Explanation:

Given equation:

`25^(2x+3) = 125^(2x+8)`

Convert 25 and 125 to base 5:

`\implies (5^2)^(2x+3) = (5^3)^(2x+8)`

Apply exponent rule
`(a^b)^c=a^(bc)`

`\implies 5^(2(2x+3)) = 5^(3(2x+8))`

If
`a^(f(x))=a^(g(x))` then
`f(x)=g(x)`:

`\implies 2(2x+3) = 3(2x+8)`

Expand:

`\implies 4x+6 = 6x+24`

Subtract 6x from both sides:

`\implies -2x+6 = 24`

Subtract 6 from both sides:

`\implies -2x=18`

Divide both sides by -2:

`\implies x=-9`