Question

$2\log_{7}(5 - 5n) + 7 = 15$
$n = \boxed{}$ type your answer...

Explanation:

Step1: Isolate the logarithmic term

Subtract 7 from both sides.
$2\log_{7}(5-5n) = 15 - 7$
$2\log_{7}(5-5n) = 8$

Step2: Simplify the coefficient of log

Divide both sides by 2.
$\log_{7}(5-5n) = \frac{8}{2}$
$\log_{7}(5-5n) = 4$

Step3: Convert to exponential form

Use $\log_b(x)=y \implies b^y=x$.
$5-5n = 7^4$
$5-5n = 2401$

Step4: Isolate the variable term

Subtract 5 from both sides.
$-5n = 2401 - 5$
$-5n = 2396$

Step5: Solve for n

Divide both sides by -5.
$n = \frac{2396}{-5}$
$n = -479.2$

Answer:

$n = -\frac{2396}{5}$ or $n = -479.2$