Question

Using logarithmic properties, what is the solution to
`log_(11)`(y + 8) +
`log_(11)`4 =
`log_(11)`60? Show all necessary steps.

Answer 1

• y = 7

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Solve the given equation:

• log₁₁(y + 8) + log₁₁4 = log₁₁60 Given
• log₁₁(y + 8) + log₁₁4 = log₁₁(15*4) Product rule
• log₁₁(y + 8) + log₁₁4 = log₁₁15 + log₁₁4 Cancel same terms
• log₁₁(y + 8) = log₁₁15 Equality rule
• y + 8 = 15
• y = 15 - 8
• y = 7