Question

zing!
2 week streak level 13
solve logarithmic equations
google classroom microsoft teams
\\(\log_{3}(4x + 5) = 2\log_{3}(5)\\)
solve the logarithmic equation.
\\(x = \square\\)

Explanation:

Step1: Apply power rule to RHS

Use $\log_b(a^c)=c\log_b(a)$:
$\log_3(4x+5)=\log_3(5^2)$

Step2: Simplify the log argument

Calculate $5^2$:
$\log_3(4x+5)=\log_3(25)$

Step3: Equate log arguments

If $\log_b(A)=\log_b(B)$, then $A=B$:
$4x+5=25$

Step4: Isolate the variable term

Subtract 5 from both sides:
$4x=25-5=20$

Step5: Solve for x

Divide by 4:
$x=\frac{20}{4}$

Answer:

$5$