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# C2 Logarithms

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1. Could a kind soul please explain to me how:
log10(y) = 3log10(x) + 2
is equivalent to:
y = 100x^3

I just need an interim step/explanation to how is works but not sure how you express it or if I'm using the correct notation. Is this right?
2. (Original post by Daebakness)
Could a kind soul please explain to me how:
log10(y) = 3log10(x) + 2
is equivalent to:
y = 100x^3

I just need an interim step/explanation to how is works but not sure how you express it or if I'm using the correct notation. Is this right?

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3. Ah thank you for the speedy reply!
4. (Original post by Daebakness)
Could a kind soul please explain to me how:
log10(y) = 3log10(x) + 2
is equivalent to:
y = 100x^3

I just need an interim step/explanation to how is works but not sure how you express it or if I'm using the correct notation. Is this right?
First of all you need to consider how to express 2 in log form.
Next up you'll need to combine logs, so remember log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b)
I hope this helps.
5. log10(y) = 3log10(x) + 2
Therefore log10(y) = log10(x^3) + log10(100) (using nlog(a) = log(a^n) and log10(100) = 2)
Therefore log10(y) = log10(x^3 x 100) (using the multiplication law)
6. Ah thanks people, helped a lot!
7. I would have done:
log10(y) - log10(x^3) = 2;
log10(y/x^3) = 2;
y/x^3 = 10^2 = 100;
y = 100x^3;

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