Recognize that this is an example of the base conversion formula for logarithms, with a = 32 and b = 10. So . Let's call the later log "x": . Now let's rewrite this in exponential form: . Next, since both 32 and 16 are both powers of 2, we'll rewrite them this way so we can have the same base: . Using a rule for exponents on the left: . This tells us that 5x = 4 or x = 4/5.
Let . Multiply both sides by : . Using a rule for logarithms we can "move" the x from in front into the argument as an exponent: . Since the log of equals the log of 16, . (We reached the same equation above, via a different route. The rest of the solution is the same.)
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