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Logarithm Help.

I'm stuck on these 3 questions.

1. Given that y= 3 x 10^2x, show that x= a log10(by), where the valies of constants a and b are to be found.

I started with writing y=log3 x log10^2x and then didn't know what to do after that.

2. Given that 2log10 (x/y)= 1+ log10(10x^2y) find the value of y correct to 3 decimal places.

I wrote 2log10(x/y)= 1+2log10x + logy and I couldn't do anything else.

3. Express this as a single logarithm.

2log10x-3log10y.

I wrote 2log10x/3log10y but it's a 3 mark question so there's something more to it. I don't know what though.
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Kareir
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Original post by Sem193
I'm stuck on these 3 questions.



3. Express this as a single logarithm.

2log10x-3log10y.

I wrote 2log10x/3log10y but it's a 3 mark question so there's something more to it. I don't know what though.


guessing you mean base 10?

Well
dont forget that
alogx=logxa a log x = log x^a

So that you actually have
logx2−logy3 log x^2 - log y^3

Then, there's one more log rule involving subtraction, remember it?

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