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# Logarithms watch

1. Hi,

Question:

3 + 2log (base 2)x = log (base 2)(10x -3)

i'm confused of what it is when u multiply outside of the brackets

and alos do not know how to change the base to 10 so can go in calculator.

thank you
2. Don't forget your logarithmic properties. For example, in the question you posted, 2 log (base 2) x = log (base 2) x^2 from the power property. And from the division property: log (base 2) (10x-3) - log (base 2) x^2 = log (base 2) [(10x-3)/x^2].

So now you have 3 = log (base 2) [(10x-3)/x^2].

And to get rid of the log (base 2) you have to do: 2^3 = 2^ (log (base 2) [(10x-3)/x^2]).

And now you're left with 8=(10x-3)/x^2 and you can just solve for x from there.

Hope it helps.

And to change the base: it's log(everything else)/log(base). For your question base is 2.

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