Final answer:
To convert the equation (1/2)^x = 1/32 to logarithmic form, we state that x is the exponent to which (1/2) must be raised to yield 1/32, resulting in the equation log_{1/2}(1/32) = x.
Step-by-step explanation:
To convert the exponential equation (1/2)ʸ = 1/32 to logarithmic form, we can make use of the basic definition of a logarithm. The definition states that if aʸ = b, then loga(b) = x. Applying this to the given equation, we recognize that 1/32 is 2 raised to the power of -5 since (1/2)-5 equals 32.
Converting the given equation to logarithmic form, we obtain:
log1/2(1/32) = x.
Here, the base of the logarithm is (1/2), which is the base of the exponential function in the given equation. By equating the logarithm to x, we are stating that x is the exponent to which the base (1/2) must be raised to get 1/32. Therefore, the logarithmic form of the equation (1/2)ʸ = 1/32 is:
log1/2(1/32) = x