Question

solving a logarithmic equation
solve: \\(\log_{4}(7t + 2) = 2\\)
\\(t = \square\\)

Explanation:

Step1: Convert log to exponential form

$\log_b(x)=y \implies b^y=x$, so $4^2=7t+2$

Step2: Calculate $4^2$

$4^2=16$, so $16=7t+2$

Step3: Isolate the term with $t$

Subtract 2 from both sides: $16-2=7t$
$14=7t$

Step4: Solve for $t$

Divide both sides by 7: $t=\frac{14}{7}$

Answer:

$t=2$