Wykaż, że jeżeli [latex] log_{5} 49=a [/latex] to [latex] log_{49} 35= frac{a+2}{2a} [/latex]

[latex]log_{5} 49=a[/latex] [latex]log_{5} 7^2=a[/latex] [latex]2log_{5} 7=a /:2[/latex] [latex]log_{5} 7= frac{a}{2}[/latex] ----------------- [latex]log_{49} 35= frac{log_535}{log_549}=[/latex] [latex]frac{log_5(5 cdot 7)}{log_549}=frac{log_55+log_57}{log_549}=[/latex] [latex]frac{1+frac{a}{2}}{a}=frac{ frac{2}{2} +frac{a}{2}}{a}=[/latex] [latex]frac{ frac{2 +a}{2}}{a}= frac{a+2}{2a}[/latex]