25 POINT PROBLEM! can someone explain to me how a to the power of log base a of b equals b?

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A logarithm is just an exponent. To be specific, the logarithm of a number x to a base b is just the exponent you put onto b to make the result equal x. For instance, since 5² = 25, we know that 2 (the power) is the logarithm of 25 to base 5. Symbolically, log5(25) = 2.log(a/b) = log a -log b, a > 0, b > 0. log an = n (log a) (Logarithm of a power). logx y = logmy / logmx (Change of base rule).The natural numbers 1, 2, 3,are respectively the logarithms of 10, 100, 1000, to the base 10. The logarithm of "0" and negative numbers are not defined.The laws apply to logarithms of any base but the same base must be used throughout a calculation. This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB.

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step-by-2step explanation: