Use properities of logarithms to solve log4x2 13log464 a x2

Use properities of logarithms to solve log₄(x+2) = 1/3log₄64

a) x=2

b) x=10

c) x=58/3

d) x=62

Solution

log4(x+2) = (1/3)log4(64)

log4(x+2) = (1/3)log4(4^3)

log4(x+2) = log4[(4^3)^1/3]

log4(x+2) = log4(4)

x+2 = 4

x = 2

Solution a)