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Simplify the following logarithmic expressions: i) log base 2 of 32, ii) log base 2 of 8

April 26, 2026Mathematics

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Answers

2 parts

\text{5}

\text{3}

Step-by-step solution

8 steps

Here are the simplifications:

Part i· 4 steps

Simplify $\log_2 32$

Let the expression be equal to $y$ .
$\log_2 32 = y$
Convert the logarithmic equation to an exponential equation.
$2^y = 32$
Express 32 as a power of 2.
$2^y = 2^5$
Equate the exponents.
$y = 5$
The simplified value is $\boxed{\text{5}}$ .

Part ii· 4 steps
$\text{3}$

Simplify $\log_2 8$

Let the expression be equal to $y$ .
$\log_2 8 = y$
Convert the logarithmic equation to an exponential equation.
$2^y = 8$
Express 8 as a power of 2.
$2^y = 2^3$
Equate the exponents.
$y = 3$
The simplified value is $\boxed{\text{3}}$ .

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