Use the Laws of Logarithms to combine the expression into a

Use the Laws of Logarithms to combine the expression into a single logarithm.

(a) log(a) + 8 log(b)

(b) ln(x^2 25) ln(x + 5)

(c) log2(6) 6 log2(x) + 1 2 log2(x + 1)

Solution

a) log(a) + 8 log(b) = log(a) + log(b)⁸ = log(ab⁸)

b) ln(x² 25) ln(x + 5) = ln[(x-5)(x+5)] - ln(x+5)

= ln(x-5) + ln(x+5) - ln(x+5) = ln(x-5)

c)  log₂(6) 6 log₂(x) + 12 log₂(x + 1) = log₂(6x⁶(x+1)¹²)