logaritmeoppgave

[mroten]

Hvordan løser man denne logaritmeoppgaven?

[tex]4lg \frac{xy^3}{x^3y}+lg \frac{x^8}{x^7}[/tex]

[ettam]

[tex]4lg \frac{xy^3}{x^3y}+lg \frac{x^8}{x^7} = lg \left(\frac{xy^3}{x^3y}\right)^4+lg \frac{x^8}{x^7} = lg \left(\frac{x^4y^{12}}{x^{12}y^4}\cdot \frac{x^8}{x^7}\right) = lg \left(\frac{x^{4+8}y^{12}}{x^{12+7}y^4}\right) = lg \left(\frac{x^{12}y^{12}}{x^{19}y^4}\right)= \underline{\underline{lg \left(\frac{y^8}{x^7}\right)}}[/tex]