Question

question 8 of 10
what is the solution to the equation below? round your answer to two decimal places.
\log_{5}(2x - 3) = 2

a. x = 11
b. x = \frac{29}{2}
c. x = 14
d. x = \frac{35}{2}

Explanation:

Step1: Convert log to exponential form

Using the definition of logarithms: if $\log_b(a) = c$, then $a = b^c$. So for $\log_5(2x - 3) = 2$, we get $2x - 3 = 5^2$.

Step2: Simplify the equation

Calculate $5^2 = 25$, so the equation becomes $2x - 3 = 25$.

Step3: Solve for x

Add 3 to both sides: $2x = 25 + 3 = 28$. Then divide by 2: $x = \frac{28}{2} = 14$.

Answer:

C. \( x = 14 \)