Question

we have log 32 to base 2 = 5 show that we get the same result by writing 32=2 power 5 and then using power rules verify the answer​

Answer 1

Answer:

Log(32) to base 2 = 5

Step-by-step explanation:

Since

2^5 = 2×2×2×2×2 = 32

So

2^5 = 32

Taking Log to base 2 on both sides we get

Log(2^5) at base 2 = Log(32) to base 2

using the power rule for logarithms we get

5(Log (2) at base 2) = Log(32) to base 2

Inter changing left and right sides we get

Log(32) to base 2 = 5(Log (2) at base 2)     ......(1)

Since Log (x) at base x = 1    for every positive integer so

Log (2) at base 2 = 1

Putting Log (2) at base 2 = 1  in equation (1) we get

Log(32) to base 2 = 5(1) = 5

Thus

Log(32) to base 2 = 5

Hence proved.

Answer 2

Answer:

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