precalculus

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log_6(2x + 4)=2?

5 In x=10?

log(x+25)=1+ log(2x-7)?

  • precalculus -

    You have to know the logarithm rules and definition
    Definition: if log(base a)x=b then x=a^b
    Rules-I am going to use base 10 but it applies for every base:
    1) loga^r=rloga
    2)log(a*b)=loga+logb
    3)log(a/b)=loga-logb
    4)change of base: loga=log(base b)a/log(baseb)10

    So the first one I don't understand question.
    Second: lnx=2 so x=e^2 (by definition)
    Third: log(x+25)-log(2x-7)=1 so by using 3rd law: log[(x+25)/(2x-7)]=1 and then definition; 10^1= (x+25)/(2x-7) so cross multiplying; 10(2x-7)=x+25 so 20x-70=x+25 19x=95 x=5
    Hope this helps

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