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# How do you calculate $\log 32$?

Last updated date: 18th Jun 2024
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Hint: The logarithm is defined as the power to which a number must be raised to obtain a particular number. For example ${\log _{10}}100 = 2$ defines that $10$ must be raised to power $2$ to obtain the number $100$. The other example is ${\log _2}8 = 3$show that $2$ must be raised to power $3$ to obtain $8$.
Here the objective is to calculate$\log 32$. To evaluate $\log 32$ write $32$ in the exponential form with the base of$2$. When the base of the logarithm is not given the base is considered naturally$2$. Then, apply the property of the logarithm to find the complete value of the$\log 32$.

Complete step by step solution:
The given expression is c $\log 32$.
Write the value of $32$ in the exponential form as a multiple of 2.
We know that $2$ multiplied $5$ times by itself is$32$. This in the exponential form is written as $32 = {2^5}$
Then, the given term $\log 32$ becomes$\log {2^5}$.
Consider the property of logarithm as,
${\log _a}{b^x} = x{\log _a}b$
Then, from the above property ${\log _2}{2^5}$is written as$\log {32^5} = 5\log 2$.
Consider the value of $\log 2 = 0.3010$.
Then, rewrite the logarithm $\log {32^5} = 5\log 2$ as,
$\Rightarrow 5\log 2 = 5\left( {0.3010} \right)$
$\therefore 5\log 2 = 1.505$

Thus, the value of $\log 32 = 1.505$

Note:
The exponent is the number of times a number can be multiplied by itself. For example consider a variable $a$ as $a \times a = {a^2}$, then ${a^n}$ represents $a$ multiplied by itself n number of times. The exponent form ${a^n}$ is pronounced as a raise to the power n. Where,
${a^0} = 1$ And ${a^1} = a$.