Question 35
Let $y=2^x$
$y^2-8y+15=0$
$(y-3)(y-5)=0$
$2^x=3$ or $2^x=5$
$x=\frac{log_{10}3}{log_{10}2}$ or $\frac{log_{10}5}{log_{10}2}$
Sum of roots$=\frac{log_{10}3+log_{10}5}{log_{10}2}=\frac{log_{10}15}{log_{10}2}$
Let $y=2^x$
$y^2-8y+15=0$
$(y-3)(y-5)=0$
$2^x=3$ or $2^x=5$
$x=\frac{log_{10}3}{log_{10}2}$ or $\frac{log_{10}5}{log_{10}2}$
Sum of roots$=\frac{log_{10}3+log_{10}5}{log_{10}2}=\frac{log_{10}15}{log_{10}2}$