b.
Multiply continuously.










Use the distributive property.

Simplify.

Subtract to the other side.

Use the third law of logarithms.

Remove the negative exponent.

Cube 4 (Simplify)

Move all the terms (containing a log) to the left-hand side of the equation.

:)
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
a)
Often one uses logarithms to solve equations where the variable is in an exponent. The exception is when you can rewrite the equation so that it says that two powers of the same number are equal. Since this equation can easily be rewritten as one power of 9 equals another power of 9:


The next step in this situation is simple and it is based on the idea that the only way two powers of 9 can be equal is if the exponents are equal. So
4x = 2
Solving this is very easy. Divide by 4:
x = 1/2

b)
Solving equations where the variable is in the argument of a logarithm usually starts with using algebra and/or properties of logarithms to transform the equation into one of the following general forms:
log(expression) = other-expression
or
log(expression) = log(other-expression)

With your equation's "non-log" term of 1, it will be more difficult to transform it into the second, "all-log" form. So we will aim for the first form.

If we can find a way to combine the two logarithms into one then we will have the first form. The two logs are not like terms so we cannot simply subtract them into one term. (Llike logarithmic terms have the same bases and the same arguments. Your logs have the same bases but the arguments are different.)

Fortunately there is another way we can combine logarithmic terms. Two properties of logarithms can be used to combine two logarithms into one: