MATHEMATICS PROBLEM SOLVER

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Thursday, 6 March 2014

LOGARITHMS C2

If log_x625 + log₃81 = 7; find x

Solution

log_x625 + log₃81 = 7

log_x625 + log₃3⁴ = 7 [81=3³ by prime factorization]

log_x625 + 4log₃3 = 7 [since log_aaⁿ= nlog_aa]

log_x625 + (4 x 1) = 7 [log_aa = 1]

log_x625 + 4 = 8

log_x625 = 8- 4

log_x625 = 4

625 = x⁴

5⁴ = x⁴ Powers cancel out

x = 5

Hence x = 5.

MATHEMATICS PROBLEM SOLVER

Thursday, 6 March 2014

LOGARITHMS C2

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