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soccergal12

solve the following: 10^(2x-3) = 0.01

  • one year ago
  • one year ago

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  1. klimenkov
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    If \(a^x=b^x\), then \(a=b\). And use \(0.01=\frac1 {100}=\frac1{10^2}=10^{-2}\).

    • one year ago
  2. klimenkov
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    Oops. Really you need is that if \(a^x=a^y\) then \(x=y\).

    • one year ago
  3. Calcmathlete
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    Use what @klimenkov said above. \[10^{2x - 3} = 0.01\]\[10^{2x - 3} = \frac{1}{100}\]\[10^{2x - 3} = \frac{1}{10^{2}}\]\[10^{2x - 3} = 10^{-2}\]\[2x - 3 = -2\]Solve for x now.

    • one year ago
  4. klimenkov
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    The very first statement is false. Forget it, because if \(2^2=(-2)^2\), but \(2\ne-2\).

    • one year ago
  5. Calcmathlete
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    What do you mean? I'm not quite following.

    • one year ago
  6. klimenkov
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    I said that mine statement was false.

    • one year ago
  7. Calcmathlete
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    Oh ok.

    • one year ago
  8. soccergal12
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    i'm sorry. which statement was false?

    • one year ago
  9. soccergal12
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    would the answer be x = 1/2

    • one year ago
  10. theyatin
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    yup

    • one year ago
  11. soccergal12
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    Thanks!

    • one year ago
  12. Calcmathlete
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    I am so late...but you are correct :)

    • one year ago
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