SOLUTION: Solve 100000^(4logx^5)

Question 628160: Solve 100000^(4logx^5)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First, what you posted is an expression. Expressions are simplified, not solved.

To simplify this we are going to transform the expression into the form

We are going to do this because no matter what "a" and "q" are.

Since the base of "log" is 10 we want to express 100000 as a power of 10. Since this is fairly easy:

The rule for exponents for a power of a power like this is to multiply the exponents:

which simplifies to:

We have almost reached the desired form of . We don't wnat the 20. Fortunately there is a property of logarithms, , which allows us to move a coefficient into the argument as its exponent:

Again we use the power of a power rule:

We now have the desired form, which simplifies to:

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