11th grade math, 6^x = 45
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11th grade math, 6^x = 45

[From: ] [author: ] [Date: 12-02-02] [Hit: ]
as a practical matter we would indicate that we were using base 10 or base e (natural) logs, since those are on the typical calculator.......
Solve for x to the nearest hundredth, 6^x = 45.

Explain if you can, please and thanks!

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Take the log (any legitimate base) of both sides:

log(6^x) = log(45)

Use the log law log(a^x) = x log(a) on the left side:

x log(6) = log(45)
x = log(45)/log(6) ≈ 2.1245 = 2.12 to the nearest hundredth.

Even though the answer is independent of the base used, as a practical matter we would indicate that we were using base 10 or base e ("natural") logs, since those are on the typical calculator.
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