Answer :

TaeKwonDoIsDead

Answer:

x = -6

Step-by-step explanation:

We recognize that 25 = 5^2 and also 125 = 5^3, thus we can write:

[tex]25^{2x+3}=125^x\\(5^2)^{2x+3}=(5^3)^x[/tex]

Now we can use the property of exponents [[tex](a^x)^y=a^{xy}[/tex]] to simplify it:

[tex](5^2)^{2x+3}=(5^3)^x\\5^{2(2x+3)}=5^{3x}\\5^{4x+6}=5^{3x}[/tex]

We equate the exponents (since we have similar base) to find the value of x:

4x + 6 = 3x

4x - 3x = -6

x = -6

kudzordzifrancis

Answer:

x=-6

Step-by-step explanation:

The given exponential equation is;

[tex]25^{2x+3}=125^x[/tex]

Rewrite both sides to base 5.

[tex]5^{2(2x+3)}=5^{3x}[/tex]

Equate the exponents;

[tex]2(2x+3)=3x[/tex]

Expand:

[tex]4x+6=3x[/tex]

Group like terms;

[tex]4x-3x=-6[/tex]

Simplify

[tex]x=-6[/tex]

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