Question 577641: Hi, i am in year 12 maths B and don't understand how to use logarithms at all. An example of a question i am having difficulty with is:
Use logarithms to solve:
7^x = 1/343
Thankyou for your help in advance
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Use logarithms to solve:
7^x = 1/343
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The name "logarithms" is unfortunate. Logs are exponents. If the name were something that implied that, it would be less confusing.
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7^x = 1/343
There are 2 ways to approach this.
If you know that 343 = 7^3, then 1/343 = 7^(-3)
Then, 7^(-3) = 1/343, and x = -3
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The 2nd method is the base change formula.
7^x = 1/343
x*log(7) = log(1/343)
x = log(1/343)/log(7)
x = -3
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