2 log 3 + 3 log 4 + 4 log 5 - 2 log 6
Mathematics
ScanSolve AI Answer
Step-by-step solution
4 stepsThe expression can be simplified using the properties of logarithms:
a log b = log (b^a)log a + log b = log (a * b)log a - log b = log (a / b)
Here are the steps:
Apply the power rule (
a log b = log (b^a)) to each term2 log 3 = log (3^2) = log 93 log 4 = log (4^3) = log 644 log 5 = log (5^4) = log 6252 log 6 = log (6^2) = log 36
Substitute these back into the original expression
log 9 + log 64 + log 625 - log 36Apply the product rule (
log a + log b = log (a * b)) for the additionslog (9 * 64 * 625) - log 36
log (576 * 625) - log 36
log (360000) - log 36Apply the quotient rule (
log a - log b = log (a / b)) for the subtractionlog (360000 / 36)
log (10000)The simplified expression is
log 10000.If the base of the logarithm is 10 (common logarithm), then
log 10000 = 4.
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