Question

lesson 25 - logarithmic functions and equ
score: 35/100 answered: 7/19
question 10
solve for x
\log_{2}(5x - 2) = 2
question help: message instructor

Explanation:

Step1: Convert log to exponential

Using the definition of logarithms: if $\log_b(a) = c$, then $b^c = a$. So for $\log_2(5x - 2) = 2$, we get $2^2 = 5x - 2$.

Step2: Solve the equation

Calculate $2^2 = 4$, so the equation becomes $4 = 5x - 2$. Add 2 to both sides: $4 + 2 = 5x$, which is $6 = 5x$. Then divide both sides by 5: $x = \frac{6}{5} = 1.2$.

Answer:

$\frac{6}{5}$ (or 1.2)