Answer:
[tex]x=\frac{4}{3}[/tex]
Step-by-step explanation:
The given logarithmic equation is
[tex]\log_{3x+4}(4096)=4[/tex]
We take antilogarithm to get:
[tex]4096=(3x+4)^4[/tex]
We write the left hand side as a power.
[tex]8^4=(3x+4)^4[/tex]
Since the exponents are the same the bases are also equal.
[tex]8=3x+4[/tex]
[tex]8-4=3x[/tex]
[tex]4=3x[/tex]
Divide both sides by 3;
[tex]x=\frac{4}{3}[/tex]
