Given 10^0.301=2 and 10^0.477= 3, solve without a calculator

Question

Given 10^0.301= 2 and 10^0.477 = 3, solve without a calculator:

a.10^x = 6

b 10^x = 8

c. 10^x = 2/3

d. 10^x =1 (solve three different ways)

Answer 1

10^a = b means that log b = a, where log means base 10 log.

So, log 2 = 0.301 and log 3 = 0.477

Therefore, log 6 = log[(2)(3)] = log2 + log3 = 0.788. That is, 10^0.788 = 6

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log 8 = log(2³) = 3log2 = 3(0.301) = 0.903 So, 10^0.903 = 8