Common logarithm question I'm studying logarithms and am doing an exercise where you're supposed to evaluate the solutions of common logarithms without using a calculator. I'm very stuck on this one particular question. I know the answer because I used my calculator, but I'd like to know how to solve it without one. The question is log((10)/(root[3](10))) How do I solve this without a calculator? (Please provide a step-by-step solution, this has really confused me.)

hotonglamoz 2022-09-24 Answered
Common logarithm question
I'm studying logarithms and am doing an exercise where you're supposed to evaluate the solutions of common logarithms without using a calculator. I'm very stuck on this one particular question. I know the answer because I used my calculator, but I'd like to know how to solve it without one. The question is
log ( 10 10 3 )
How do I solve this without a calculator? (Please provide a step-by-step solution, this has really confused me.)
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Answers (2)

Madden Huber
Answered 2022-09-25 Author has 12 answers
Hint
10 10 3 = 10 10 1 / 3 = 10 1 1 / 3 = 10 2 / 3
Now, what would the logarithm (assuming base 10) of that final expression be?
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Zack Chase
Answered 2022-09-26 Author has 3 answers
Remember that the logarithm of a quotient is the difference of logarithms:
l o g ( 10 10 3 ) = l o g ( 10 ) l o g ( 10 3 ) = 1 l o g ( 10 1 / 3 ) = 1 1 3 l o g ( 10 ) = 1 1 3 = 2 3
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