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Question

Write the expression as a single logarithm.

4log₆x-1/5 log₆z + 2log₆y

Answer 1

4 log₆ x - (1/5) log₆ z + 2 log₆ y

Use the Power Law for logarithms:

c log_b a = log_b a^c

= log₆ x⁴ - log₆ z^1/5 + log₆ y²

Use the Sum & Difference Laws for logarithms:

log_b a + log_b c = log_b ac

log_b a - log_b c = log_b (a/c)

Rearrange the terms:

= log₆ x⁴ + log₆ y² - log₆ z^1/5

= log₆ [(x⁴y²)/z^1/5]

Answer 2

Write the expression as a single logarithm.

4log₆x-1/5 log₆z + 2log₆y

log (x)^4-log(z)^1/5+log(y)^2

log(x)^4+log(z)^(1/5)(y)^2

Log ((x^4)/((z)^(1/5)(y)^2)