Answer:
x = 4
Step-by-step explanation:
When you have a coefficent in front of a logarithm function, you can take the argument to the power of that coefficient. For example, the 3 in front of the logarithm can be brought into the argument, and you can take 'x' to the third power. You get:
[tex] log_{4}( {x}^{3} ) = log_{4}(32) + log_{4}(2) [/tex]
When you add logarithms, it is equivalent to multiplying their arguments:
[tex]log_{4}( {x}^{3} ) = log_{4}(32 \times 2) = log_{4}(64) [/tex]
Since both sides are log base 4, the arguments must equal each other:
[tex] {x}^{3} = 64[/tex]
[tex]x = \sqrt[3]{64} = 4[/tex]
