$\lg 10^a=a$

$10^{\lg a}=a$

Oppgave 1

  • \begin{align}\lg 10
    &= \lg 10^1\\
    &=1
    \end{align}

  • \begin{align}\lg 100 &= \lg 10^2\\
    &=2
    \end{align}

  • \begin{align}
    \lg 1000 &=\lg 10^3\\
    &=3\lg 10\\&=3
    \end{align}

  • \begin{align}\lg 1
    &= \lg 10^0\\
    &=0
    \end{align}

Oppgave 2

Bruk definisjonen for å finne verdien til logaritmene.

Det kan være lurt å tenke potenstall…..

  • \begin{align}\lg 0,1
    &= \lg 10^{-1}\\
    &=-1
    \end{align}

  • \begin{align}\lg 0,01 &= \lg 10^{-2}\\
    &=-2
    \end{align}

  • \begin{align}\lg 0,001
    &= \lg 10^{-3}\\
    &=-3
    \end{align}

  • \begin{align}&\lg 0\\
    \text{finnes ikke }
    \end{align}

Oppgave 3

Bruk definisjonen for å finne verdien til logaritmene.

  • \begin{align}\lg \sqrt{10}
    &= \lg 10^{\frac{1}{2}}\\
    &=\frac{1}{2}
    \end{align}

  • \begin{align}\lg \sqrt{10} = \end{align}

  • \begin{align}\lg 10^{\frac{2}{3}}=\frac{2}{3}\end{align}

Oppgave 4

Bruk definisjonen for å finne verdien til logaritmene.

  • \begin{align}
    10^{\lg 10}
    &=10
    \end{align}

  • \begin{align}
    10^{\lg 0.5}
    &=10^{\lg \frac{1}{2}}\\
    &=\frac{1}{2}
    \end{align}

  • \begin{align}
    10^{(\lg 2+\lg 3)}
    &=10^{\lg(2\cdot 3)}\\
    &=6
    \end{align}

Oppgave 5

$\lg(xy)+\lg x=$

$\lg x^2+\lg xy-\lg y=$

Bruk reglen for å forenkle logaritmen.

  • \begin{align}
    10^{2\lg 5}
    &=10^{\lg 5^2}\\
    &=25
    \end{align}

  • \begin{align}
    10^{3\lg 2}
    &=10^{\lg 2^3}\\
    &=8
    \end{align}

  • \begin{align}
    10^{\frac{\lg 9}{2}}
    &=10^{\lg 3}\\
    &=3
    \end{align}

    \begin{align}
    \frac{\lg 9}{2}
    &=\frac{1}{2}\lg 9\\
    &=\lg 9^{1}{2}\\
    &=\lg \sqrt{9}\\
    &=\lg 3
    \end{align}

  • \begin{align}
    10^{\frac{\lg 64}{3}}
    &=10^{\lg 4}\\
    &=4
    \end{align}

    \begin{align}
    \frac{\lg 64}{3}
    &=\frac{1}{3}\lg 4^3\\
    &=\lg 4^{3\cdot \frac{1}{3}}\\
    &=\lg 4
    \end{align}

Oppgave 6

  • \begin{align}
    \lg \sqrt[3]{x}+\lg \sqrt[3]{x^2}
    &=\lg x^{\frac{1}{3}}+\lg x^{\frac{2}{3}}\\
    &=\lg (x^{\frac{1}{3}}\cdot x^{\frac{2}{3}})\\
    &=\lg (x^{\frac{1}{3}+\frac{2}{3}})\\
    &=\lg x
    \end{align}

  • \begin{align}
    \lg x^2y-\lg y
    &=2\lg x+\lg y-\lg y\\
    &=2\lg x
    \end{align}

  • \begin{align}\lg \sqrt{x^3}=\end{align}

  • \begin{align}\lg(x^2)^3=\end{align}

  • \begin{align}\lg 2x^3=\end{align}

  • \begin{align}
    \lg \frac{x^2}{y^2}+\lg\frac{y}{x}
    &=
    \end{align}

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