Question

Solve for x in the following equation.

Answer 1

$\huge\text{Hey there!}$

$\mathsf{5^{x - 2} = 5^8}$

$\mathsf{5^{x - 2} = 5\times5\times5\times5\times5\times5\times5\times5}$

$\mathsf{5^{x - 2} = 25\times25\times25\times25}$

$\mathsf{5^{x - 2} = 625\times625}$

$\mathsf{5^{x - 2} =390,625}$

$\large\textsf{Solving for the exponent:}$

$\mathsf{5^{x - 2} =390,625}$

$\large\textsf{Take the log (logarithm) to both of the sides:}$

$\mathsf{log(5^{x - 2} \rightarrow log(390,625)}$

$\large\textsf{Simplify it:}$

$\mathsf{(x - 2) \times(log (5)) \rightarrow log(390,625)}$

$\large\textsf{Simplify that as well:}$

$\mathsf{x - 2 = \dfrac{log(390,625)}{log(5)}}$

$\large\textsf{You get it: }\mathsf{x - 2 = 8}$

$\large\textsf{ADD by 2 to BOTH of the SIDES:}$

$\mathsf{x - 2 + 2 = 8 + 2}$

$\large\textsf{Simplify it:}$

$\mathsf{x = 8 + 2}$

$\mathsf{x = 10}$

$\huge\textsf{Therefore, your answer should be:}$

$\huge\boxed{\mathsf{x =} \frak{10}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$

Answer 2

Answer:

$\fbox{x=10}$

Step-by-step explanation:

Given:

${5}^{x - 2} = {5}^{8}$

Since base of both the equivalent is same hence the exponent will also be equal to each other.

Comparing the exponent of LHS & RHS,

$x-2 =8$

adding 2 on both the side,

$x-2+2= 8+2$

$\fbox{x=10}$

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