SOLUTION: Solve the equation {{{log(16,(x))+log(8,(x))+log(4,(x))+log(2,(x))=6}}}

Question 143992: Solve the equation
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Use the change of base formula to rewrite each individual log. Remeber the change of base formula is

Rewrite 16 as . Rewrite 8 as . Rewrite 4 as

Rewrite the each denominator using the identity

Multiply both sides by the LCD . Doing this will eliminate the denominators.

Distribute and multiply

Factor out the GCF

Add

Rearrange the terms

Rewrite the expressions using the identity

Since the logs have the same base, this means that the argument (the terms inside the log) are equal.

Take the 50th root of both sides

So our answer is which is approximately

note: can be written as =

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