Question

㏒ 2 =0.3010 then ㏒ 1 ÷2 is
step by step explation

Answer 1

Let us assume that there are suitable values that satisfy,

$\cdots\longrightarrow a^{x}=b.$

However, as logarithm finds the exponent,

$\text{ \cdots\longrightarrow\boxed{x=\log_{a}b.}\ \cdots(1) }$

Let us take the same exponents on both sides.

Then,

$\cdots\longrightarrow a^{mx}=b^{m}.$

But this is equivalent to,

$\text{ \cdots\longrightarrow \boxed{mx=\log_{a}{b^{m}}.}\ \cdots(2) }$

We have,

$\text{ \cdots\longrightarrow\underline{m\log_{a}b=\log_{a}{b^{m}}.} [Properties of logarithms.]}$

Now, we have,

$\text{ \cdots\longrightarrow\log_{}{\dfrac{1}{2}}=\log_{}{2^{-1}} }$

$\text{ \cdots\longrightarrow\log_{}{2^{-1}}=-\log_{}{2} }$

$\cdots\longrightarrow-\log_{}{2}=\underline{-0.3010}.$

The required value is $\boxed{-0.3010}$.