Question

The equation log ₂ 32=5 can be written in the form 2ᵃ =b where:

A) a=5,b=32
B) a=32, b=5
C) a=5, b=2
D) a=2, b=5

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf log_2\:32 = 5$}`

`\Large \text{$ \sf 2^a = b$}`

`\Large \text{$ \sf 2^5 = 32$}`

`\Large \boxed{\boxed{\text{$ \sf a = 5,\:b = 32$}}}`

Answer 2

The equation log ₂ 32=5 can be rewritten in exponential form as 2^5 = 32, which correlates with option A) a=5, b=32. This is due to the basic property of logarithms where the base raised to the logarithm result equals the number.

Step-by-step explanation:

The equation log ₂ 32 = 5 can be transformed into an exponential form using the base 2, where the exponent on the base equals the logarithm result. According to the properties of logarithms, if log base (b) of a number (n) equals x, then the equation can be rewritten as b to the power of x equals n (bx = n). In this case, since 2 raised to the power of 5 equals 32 (25 = 32), we can derive the correct transformation.

Therefore, options A through D can be evaluated and in this context, option A) a = 5, b = 32 is the correct way to express the given logarithmic equation in an exponential form, satisfying the equation 2a = b.