Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

write the expression as a single logarithm and simplify?

log *b*3x+4(log*b*x-log*b*y)

*b*=subscript

6 Answers

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  • 1 decade ago
    Favorite Answer

    First look at log*b*x-log*b*y and simplify this. Since the operation is subtraction, you can combine this into a single logarithm through division. It equals log*b*(x/y). So now we have:

    log*b*3x+4(log*b*(x/y))

    The 4 becomes the exponent on (x/y), giving us

    log*b*3x+log*b*(x/y)^4

    Now, these two expressions can be combined into a single log function through multiplication since they are being added, giving us:

    log*b*(3x)(x/y)^4.

    We can simplify (3x)(x/y)^4 further. (x/y)^4=(x^4)/(y^4).

    (3x)(x^4)=3x^5, so the final answer is:

    log*b*((3x^5)/(y^4))

  • maussy
    Lv 7
    1 decade ago

    you use formula

    log*b* a +log*b* c = log*b* ac and

    log*b* a -log*b* c = log*b* a/c and

    log*b* a^c = c log *b*a

    so the expression is

    log*b*(3x *(x/y)^4)

    log*b* (3x^5/y^4)

  • 1 decade ago

    All logs are to the base 'b' - I will just write log

    log(3x) + 4(log x - log y)

    =log(3x) + 4log(x/y) ----- log a - log b = log(a/b)

    =log(3x) + log(x/y)^4 ---- nlog(a) = log(a^n)

    =log(3x.(x/y)^4)) ------ log(a) + log(b) = log(ab)

    =log(3x^5 / y^4)

  • 1 decade ago

    log *b* ((3x^5)/(y^4))

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  • Anonymous
    1 decade ago

    log*b* ((3x+4)+(x/y))

  • 1 decade ago

    log*b*3x^5y^(-4)

    *b*=subscript

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