Evaluate each logarithmic expression a log3 Squareroot 27 b

Evaluate each logarithmic expression. (a) log_3 Squareroot 27 (b) log_2 80 - log_2 10 (c) log_8^4 (d) log_6^4 + log_6^9 Use the Laws of Logarithms to expand the expression. log 3 Squareroot x + 2/x^4(x^2 + 4) Combine into a single logarithm: ln x - 2 ln(x^2 + 1) + 1/2 ln(3 - x^4)

Solution

a) log3(sqrt27)

log3(3^3)

3log3(3) = 3log3/log3 = 3

b) log2(80) - log2(10)

log2(80/10) = log2(8)

log2(2^3) = 3log2/log2 =3

c) log8(4) = log4/log8

= log2^2/log2^3

= 2log2/3log2

= 2/3

d) log6(4) +log6(9)

log6(9*4)

log6(36)

log6^2/log6

= 6