Question

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

Answer 1

Answer:

$x = -9$

Step-by-step 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:

$\implies x=-9$

Answer 2

Let's solve up

$\\ \rm\rightarrowtail 25^{2x+3}=125^{2x+8}$

$\\ \rm\rightarrowtail 5^{2(2x+3)}=5^{3(2x+8)}$

$\\ \rm\rightarrowtail 5^{4x+6}=5^{6x+24}$

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

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

$\\ \rm\rightarrowtail x=-9$