More Exponential Equations

Discussion in 'Algebra' started by nycmathguy, Jul 3, 2022.

  1. nycmathguy

    nycmathguy

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    Solve 5^(x + 1) + 10^(x - 1) = 15^(2x - 1)
     
    nycmathguy, Jul 3, 2022
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  2. nycmathguy

    MathLover1

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    Solving Exponential Equations:
    Step 1: Express both sides in terms of the same base.
    Step 2: Equate the exponents.
    Step 3: Solve the resulting equation.
    Solve. ...

    or
    Step 1: Isolate the exponential and then apply the logarithm to both sides.

    or
    sometimes have to use calculator


    5^(x + 1) + 10^(x - 1) = 15^(2x - 1)

    5^(x + 1) =5*5^x

    10^(x - 1)=(5^x*2^x)/10

    15^(2x - 1)=15^(2x)/ 15 =(3^(2x)*5^(2x))/15

    5*5^x +(5^x*2^x)/10=(3^(2x)*5^(2x))/15 ...........simplify

    2 *45^x = 3 (2^x + 50)..........use calculator and you get

    x≈1.14557

    [​IMG]
     
    MathLover1, Jul 3, 2022
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    Beautifully done.
     
    nycmathguy, Jul 3, 2022
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