Mathematics

Mathematics

Problem

Use the definition of the logarithmic function to find xx. a. log⁡x1000=3\log_x 1000 = 3 b. log⁡x25=2\log_x 25 = 2
Intuitive explanation

The logarithmic function and exponential function are inverses of each other—so the definition of log⁡b(a)=c\log_b(a) = c really just means bc=ab^c = a. To find xx, convert the logarithmic equation into its exponential form, then solve for xx using algebra. This flips the problem from "what power?" into "what number?" which is usually much more straightforward.

Intuitive explanation

The logarithmic function and exponential function are inverses of each other—so the definition of log⁡b(a)=c\log_b(a) = c really just means bc=ab^c = a. To find xx, convert the logarithmic equation into its exponential form, then solve for xx using algebra. This flips the problem from "what power?" into "what number?" which is usually much more straightforward.

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