Logs and solving

Question

Solve log(subscript 1/2) 32

Answer 1

log of 32 to the base 1/2 is x where 1/2 to the x power = 32

(1/2)^x =32 or 1/2^x =32

2^x = 1/32

That has to be a negative number

32 = (1/2)^x

1/2 raised to the x power = 32

2 cubed = 8

2 squared =4

4x8 = 32

2⁵ = 32 2³ times 2² = 2⁵ just add the exponents

x=-5, negative 5 because the 2 is in the denominator

(1/2)^-5 = 2⁵ = 32 The negative exponent flips the base upside down

log_1/232 = -5

(1/2)^-5 = 32