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    Solve

    8^y = 4^(2x+3)
    and
    log 2y = log 2x + 4

    Thanks
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    solve for what? x? y?
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    (Original post by Amrad)
    Solve

    8^y = 4^(2x+3)
    and
    log 2y = log 2x + 4

    Thanks
    (2^3)y = (2^2)^(2x+3)
    2^3y = 2^2(2x+3)
    2^3y = 2^(4x+6)
    3y=4x+6
    y = (4x+6)/3

    log2y = log2x + 4

    You can now use a substitution to obtain a logarithmic equation in one variable. Transform it into the form log[something] = [something] which you can then solve.
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    (Original post by Amrad)
    Solve

    8^y = 4^(2x+3)
    and
    log 2y = log 2x + 4

    Thanks
    err... first equation is simple indicies rules...
    8^y=2^3y
    4^(2x+3)=2^2(2X+3)...

    check your indicies rules... then.. equate them...
    8^y=4^(2x+3)
    2^3y=2^2(2X+3)

    Take Log base 2 both sides... 3y=2(2X+3)
    So... 3y=4X+6


    SECOND EQUATION THERE IS A PROBLEM... do you mean
    log 2y = (log 2x) + 4 OR log 2y = log (2x+4)

    For FORMER one.... log 2y = (log 2x) + 4
    Take power of 10... assuming you mean log base 10...
    10^log 2y =10^((log 2x) + 4)
    2y = 2X times 10^4
    So.... y = 10000X

    For LATTER ONE... log 2y = log (2x+4)
    you base 10 on both sides...
    so 2Y=2X+4.... so Y=X+2

    NOW COMBINE FIRST & SECOND RESULTS

    For 3y=4X+6 and y = 10000X...
    X = 3/14998 and Y= 15000/7999

    For 3y=4X+6 and Y=X+2...
    X = 0 and Y = 2

    MAKE SURE YOU MAKE CLEAR WHAT YOU MEAN... !!!
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    (Original post by anchemis)
    err... first equation is simple indicies rules...
    8^y=2^3y
    4^(2x+3)=2^2(2X+3)...

    check your indicies rules... then.. equate them...
    8^y=4^(2x+3)
    2^3y=2^2(2X+3)

    Take Log base 2 both sides... 3y=2(2X+3)
    So... 3y=4X+6


    SECOND EQUATION THERE IS A PROBLEM... do you mean
    log 2y = (log 2x) + 4 OR log 2y = log (2x+4)

    For FORMER one.... log 2y = (log 2x) + 4
    Take power of 10... assuming you mean log base 10...
    10^log 2y =10^((log 2x) + 4)
    2y = 2X times 10^4
    So.... y = 10000X

    For LATTER ONE... log 2y = log (2x+4)
    you base 10 on both sides...
    so 2Y=2X+4.... so Y=X+2

    NOW COMBINE FIRST & SECOND RESULTS

    For 3y=4X+6 and y = 10000X...
    X = 3/14998 and Y= 15000/7999

    For 3y=4X+6 and Y=X+2...
    X = 0 and Y = 2

    MAKE SURE YOU MAKE CLEAR WHAT YOU MEAN... !!!
    Indeed!

    log 2y = (log 2x) + 4 is a fair bit more tricky to deal with than

    log 2y = log (2x+4) !!

    Argh!
    Aitch
 
 
 
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