Question

Value of log square root 24

Answer 1

Answer:

4.89897948557

is it the answer

Answer 2

The value of $\log \sqrt{24}$ = = 0.69010625

Step-by-step explanation:

We have,

$\log \sqrt{24}$

To find, the value of $\log \sqrt{24}$ = ?

∴ $\log \sqrt{24}$

= $\log 24^{\dfrac{1}{2}}$

Using the logarithm identity,

$\log a^{m}=m\log a$

= $\dfrac{1}{2}\log 24$

= $\dfrac{1}{2}\log (2^3\times 3)$

Using the logarithm identity,

$\log (a\times b) = \log a+\log b$

= $\dfrac{1}{2}(\log 2^3+ \log3)$

= $\dfrac{1}{2}(3\log 2+ \log3)$

∵ $\log 2$ = 0.30103 and $\log 3$ = 0.4771225

= $\dfrac{1}{2}(3\times 0.30103+ 0.4771225)$

= $\dfrac{1}{2}(0.90309+ 0.4771225)$

= $\dfrac{1}{2}(1.3802125)$

= 0.69010625

∴ The value of $\log \sqrt{24}$ = = 0.69010625