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Math Help - Simplifying with laws of logarithms

  1. #1
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    Simplifying with laws of logarithms

    I am currently studying engineering level 3 NVQ and have been having problems with logarithms, the problems I have been given I don't understand these are:

    Use laws of logarithms methods to simplify and evaluate the equation given:

    Simplify 5n = 7 x 2n, rearrange and make n the subject


    also another problem is

    Simplify θ = 250 x e-0.05 x t and make t the subject


    and continuing from that:

    what is the value of t when θ = 195C



    Thanks in advance
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  2. #2
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    Re: Simplifying with laws of logarithms

    Quote Originally Posted by Scottrich12 View Post
    I am currently studying engineering level 3 NVQ and have been having problems with logarithms, the problems I have been given I don't understand these are:

    Use laws of logarithms methods to simplify and evaluate the equation given:

    Simplify 5n = 7 x 2n, rearrange and make n the subject


    also another problem is

    Simplify θ = 250 x e-0.05 x t and make t the subject


    and continuing from that:

    what is the value of t when θ = 195C



    Thanks in advance
    For problem number one there are many ways to solve it. Here is one

    5^n=7 \cdot 2^n \iff \frac{5^n}{2^n}=7

    \left( \frac{5}{2}\right)^n=7

    Now if we take the natural logarithm of both sides we get

    \ln\left( \frac{5}{2}\right)^n=\ln(7) \iff n\ln\left( \frac{5}{2}\right)=\ln(7)

    Solving for n gives

    n=\frac{\ln(7) }{\ln\left( \frac{5}{2}\right)}

    Now you try the 2nd one and remember that \ln( e^{t})=t
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  3. #3
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    Re: Simplifying with laws of logarithms

    How would this be written as log to the base 10?
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  4. #4
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    Re: Simplifying with laws of logarithms

    Quote Originally Posted by Scottrich12 View Post
    How would this be written as log to the base 10?
    you've posted this problem twice ...

    Laws of Logarithms HELP!

    ... in future, please refrain from double posting.
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