Question

Without using log, Solve for x. a1" title="25^{2x+3} = 125^{x}" alt="25^{2x+3} = 125^{x}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

x=-6

Step-by-step explanation:

The given exponential equation is;

$25^{2x+3}=125^x$

Rewrite both sides to base 5.

$5^{2(2x+3)}=5^{3x}$

Equate the exponents;

$2(2x+3)=3x$

Expand:

$4x+6=3x$

Group like terms;

$4x-3x=-6$

Simplify

$x=-6$

Answer 2

Answer:

x = -6

Step-by-step explanation:

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

$25^{2x+3}=125^x\\(5^2)^{2x+3}=(5^3)^x$

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

$(5^2)^{2x+3}=(5^3)^x\\5^{2(2x+3)}=5^{3x}\\5^{4x+6}=5^{3x}$

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

4x + 6 = 3x

4x - 3x = -6

x = -6