Question

Find the value of
$i){\log }_{2}32$ $ii){\log }_5\sqrt[3]{35}$
$iii){\log }_{\sqrt{2}}64$ $iv){\log }_{10}100000$

Answer 1

# $\left(i\right)lo{g}_{2}32=x$

$32=2^x$ $x=5$

$\left(ii\right)lo{g}_{5}3\sqrt{5}=x$

$3\sqrt{5}=5^x\Rightarrow (5{)}^{1/3}=5^x$

$x=1/3$

$\left(iii\right)lo{g}_{\sqrt{2}}64=x$

$64=(\sqrt{2}{)}^x\Rightarrow 64=2x/2$

$x=14$

$\left(iv\right)lo{g}_{10}100000=x\Rightarrow 10,0000={10}^x$

$x=5$