Question

lesson 26 - solving logarithmic equations
score: 25/100 answered: 5/20
question 6
solve exactly.
\\(\log_{7}(12x) = 3\\)
\\(x = \\)
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 $\log_7(12x) = 3$, we get $7^3 = 12x$.

Step2: Calculate $7^3$

$7^3 = 7\times7\times7 = 343$, so the equation becomes $343 = 12x$.

Step3: Solve for x

Divide both sides by 12: $x = \frac{343}{12}$.

Answer:

$\frac{343}{12}$