To solve the equation [tex]\( 5^{(6x - 9)} = 125 \)[/tex], we follow these steps:
1. Rewrite 125 as a power of 5:
[tex]\[
125 = 5^3
\][/tex]
So, the equation becomes:
[tex]\[
5^{(6x - 9)} = 5^3
\][/tex]
2. Equate the exponents of the equation:
Since the bases are the same, the exponents must be equal:
[tex]\[
6x - 9 = 3
\][/tex]
3. Add 9 to each side:
To solve for [tex]\( x \)[/tex], we first isolate the term with [tex]\( x \)[/tex]:
[tex]\[
6x - 9 + 9 = 3 + 9
\][/tex]
Simplifying, we get:
[tex]\[
6x = 12
\][/tex]
4. Divide each side by 6:
Finally, to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{6x}{6} = \frac{12}{6}
\][/tex]
Simplifying, we get:
[tex]\[
x = 2
\][/tex]
So, the step-by-step solution is as follows:
1. Rewrite 125 as a power of 5
2. Equate the exponents of the equation
3. Add 9 to each side
4. Divide each side by 6
