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    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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    (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
     a log x = log x^a

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

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

    Spoiler:
    Show

     log a - log b = log \dfrac {a}{b} 



meaning that the answer is log\dfrac{x^2}{y^3}
 
 
 
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