Use a calculator and the Change-of-Base Formula to find the logarithm. Round your answer to four decimal places. log7 3

Question

log₇ 3

Answer 1

log₇ 3

Log 3 base 7

log₇ 3 = x

if you Log both sides you get

7^x = 3

Log 7^x = Log 3

xLog 7 = Log 3

X = Log₁₀ 3 / Log₁₀ 7

Answer

Log₁₀ (7) = 0.845

Log₁₀ (3) = 0.477

Log (3) / Log (7)

= 0.477 / 0.845

= 0.5646

Also, in Excel

Log (3,7) = 0.5646

Answer 2

The change of base formula here gives log₇ 3 = (log₁₀ 3)/(log₁₀ 7) = 0.4771/0.8451 = 0.5645.