Solve log₁₁(y + 8) + log₁₁4 = log₁₁60

Solution:

Given expression is

log₁₁(y + 8) + log₁₁4 = log₁₁60.

Log_axy = log_ax + log_ay

Therefore we can state:

log₁₁(y + 8) + log₁₁4 = log₁₁[(y + 8) × 4]

Since log₁₁(y + 8) + log₁₁4 = log₁₁60,

log₁₁4(y + 8) = log₁₁ 60

Which implies

4(y + 8) = 60

y + 8 = 60/4

y + 8 = 15

y = 15 - 8

y = 7

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Solve log₁₁(y + 8) + log₁₁4 = log₁₁60

Summary:

Solving log₁₁(y + 8) + log₁₁4 = log₁₁60, we obtain y = 7