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    sim0nz12345's Avatar
    sim0nz12345 Posts: 77, Reputation: 2
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    #1

    Aug 18, 2007, 08:38 PM
    Logorithmic and exponontial functions
    How would you solve these simultaneous equations:

    y=10^(x)-2 and
    y=log10(x+2), x>0

    log10, the 10 being the base of the log function

    Thank you
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Aug 19, 2007, 01:33 PM
    One thing to notice is that these 2 equations are actually quite similar. The second one can be re-arranged to give:

    x= 10^y - 2.

    So from this you can see that x=y.

    This then leads you to solve:

    x = 10^x - 2

    Now this one I don't believe has a closed-form solution. You can get an approximation of the answer using a technique such as Newton's method, or just plug away on your calculator and you can get as many digits of accuracy as you'd like. Hint -the answer is less than 0.5.
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