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Math Help - solving for y in terms of x

  1. #1
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    solving for y in terms of x

    i dont know how to go about this problem, solve the following for y in terms of x: 10^y=5^x-3
    thank you!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mxhockey140 View Post
    i dont know how to go about this problem, solve the following for y in terms of x: 10^y=5^x-3
    thank you!
    Before I proceed, is it 10^y=5^{x-3} or 10^y=5^x-3?
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  3. #3
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    its the first one x-3 is the exponent
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mxhockey140 View Post
    its the first one x-3 is the exponent
    The way to do this involves taking the natural log of both sides:

    10^y=5^{x-3}\implies \ln\left(10^y\right)=\ln\left(5^{x-3}\right)

    Using power rules, we can rewrite this as y\ln\left(10\right)=\left(x-3\right)\ln\left(5\right)

    Can you take it from here?
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  5. #5
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    no not really.. im not the best with this stuff.
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  6. #6
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    Quote Originally Posted by mxhockey140 View Post
    no not really.. im not the best with this stuff.
    If you're attempting questions involving exponentials and logarithms it's expected that you can make y the subject by solving what is essentially a linear equation.

    Can you solve a y = b (x - 3) for y?
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  7. #7
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    thats why i was looking for help..
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  8. #8
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    Quote Originally Posted by mxhockey140 View Post
    thats why i was looking for help..
    I would have assumed that you were looking for help in getting from the original equation to a stage where you could reasonably be expected to complete the solution.

    Since another question you've asked (http://www.mathhelpforum.com/math-he...28-curves.html) strongly suggest that you're studying calculus, your trouble in solving a linear equation is surprising and of concern.

    I ask again:

    Can you solve for y?

    What about solving 3y = 4(x - 3) for y?

    If you cannot at least do this last one then I would suggest that your real problem is an insufficient grasp of the mathematical knowledge prerequisite to the topic you're currently being taught. In which case you're strongly advised to go back and revise that material in collaboration with your instructor.
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