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Try Try this:We know log2 32=5. Show that we get thesame result by writing 32= 2⁵ and then usingpower rules. verify the answer. |
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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. |
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