Solve for x to the nearest hundredth, 6^x = 45.
Explain if you can, please and thanks!
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.
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.