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Question

Given that 2^a = 3 and 2^b = 5 find the logarithm in terms of a, b, or both

log 75
2 ( tried to make that show it's the base.) show step by step i dont get it!

Answer 1

First, you need to realize that logarithm is the inverse of exponentiation, just like subtraction is the inverse of addition.

Thus: 10 ^ 2 = 100, and log 100 = 2. Thus, if you take log(a) a^b, the answer will be b.

For 2^a = 3:
log(2) 2^a = log(2) 3
a = log(2) 3

For 2^b = 5:
log(2) 2^b = log(2) 5
b = log(2) 5

Answer 2

undergo in recommendations, logs are inverse exponents log(base a) b = c potential a^c = b So take log (base 4) 16 4 to what ability equals 16 ... 2 for sure log (base 40 9) 7 40 9 to what ability is 7 a million/2 even as no base is written, it really is theory to be 10 10 to what ability is a million,000,000 6