Question

logarithm of a number is -2×1/4 and log 5.623 = 0.7500 find the number

Answer 1

Answer:

Keep in mind

$\log_{a}b=\frac{\log b}{\log a}$

Let the number be A.

It is not given that the log has either base e, or base 10.

$\log_{e}A=-2\times \frac{1}{4}\\\\ \log_{e}A=\frac{-1}{2}\\\\ \log A=\frac{-1}{2}*\log e\\\\ A=e^{\frac{-1}{2}}\\\\ A=\frac{1}{\sqrt{2.72}},\\\\ A=0.6060..{\text{or}}  \\\ \log_{10}A=-2\times \frac{1}{4}\\\\ \log_{10}A=\frac{-1}{2}\\\\ \log A=\frac{-1}{2}*\log 10\\\\ A=(10)^{\frac{-1}{2}}\\\\ A=\frac{1}{\sqrt{10}}\\\\ A= 0.316$

So, the number is either

0.606060......

or, 0.3162

Depending upon the base of logarithm whether it is e, or 10.