Without using logarithm tables, evaluate: ${log}_{15} 225^{225}$

Open in App

Solution

We can write: $225 = 15^{2}$
So $225^{225} = (15^{2})^{225}$
$l o g_{15} 225^{225} = l o g_{15} (15^{2})^{225}$
we know that $l o g_{a} a^{n} = n l o g_{a} a = n$
So $l o g_{15} 15^{225 \times 2} = 225 \times 2 = 450$

Suggest Corrections

Similar questions

{log}_{2} {log}_{2} {log}_{2} 16

{log}_{2 \sqrt{3}} 1728

l o g_{10} 25 = x, l o g_{10} 75 = y

x, y

l o g 10^{3},

l o g 10^{2}

{(6.32)}^{2} \times \sqrt[4]{83.94}

\frac{(17.42)^{2 / 3} \times 18.42}{\sqrt{126.37}}

Join BYJU'S Learning Program