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Explain the error in the solution below. What additional step needs to be completed?

log x – log53 = 2log53
log x = 3log53
log x = log533
x = 27

1 Answer

5 votes
The solution above has an error in the last step. When one tries to solve for x, they must use the definition of logarithms to get back to x. The error lies in the fact that taking the logarithm of a number to a power is not the same as raising that logarithm to that power.

So, instead of:

log x = log533

x = 27

It should be:

x = 53^3 = 125^2 = 15,625

Therefore, the additional step that needs to be completed is to use the definition of logarithms to find x.
User Leo Farmer
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