Question

$10 {2}^{y} = 25 \: find \: y$


10^2y=25 find y correct answer will be marked as brainliest. 10raises to power2y=25​

Answer 1

$\Large\text{\underline{\underline{Explanation}}}$

The given equation: -

$\cdots\longrightarrow10^{2y}=25.$

We can express the exponent in terms of logarithms, -

$\cdots\longrightarrow10^{2y}=25\iff 2y=\log_{10}25.$

Further simplifying, -

$\cdots\longrightarrow2y=2\log_{10}5.\ [\because\log a^{m}=m\log a]$

$\text{ \cdots\longrightarrow\boxed{y=\log_{10}5} }$

$\Large\text{\underline{\underline{More information}}}$

Power notations and logarithms

$\text{ \cdots\longrightarrow\boxed{a^{x}=N\iff x=\log_{a}N.} }$

Properties of logarithms

$\text{ \cdots\longrightarrow\boxed{\begin{aligned}&(1)\log_{a}b=\dfrac{\log_{c}a}{\log_{c}b}.\\\\&(2)\log_{a}b=\dfrac{1}{\log_{b}a}.\\\\&(3)\log_{a}b\cdot\log_{b}a=1.\\\\&(4)\log_{a^{m}}b^{n}=\dfrac{n}{m}\log_{a}b.\\\\&(5)a^{\log_{c}b}=b^{\log_{c}a}.\end{aligned}} }$