Question

log4 2+ log4 32 is equal to​

Answer 1

Given,

A logarithmic expression log₄2 + log₄32

To Find,

The value of the logarithmic expression

Solution,

By using the property of logarithm we can change its base as

log₄2 = 1/2 log₂2 = 1/2

log₄32 = 1/2 log₂32 = 5/2

Now, after adding up these values we get,

log₄2 + log₄32 = 1/2 + 5/2

                         = 6/2

                         = 3

Hence, the value of log₄2 + log₄32 is 3.

Answer 2

$\displaystyle \sf{ log_{4}(2) + log_{4}(32) } = 3$

Given :

$\displaystyle \sf{ log_{4}(2) + log_{4}(32) }$

To find :

To simplify the expression

Formula :

We are aware of the formula on logarithm that

$\sf{1. \: \: \: log( {a}^{n} ) = n log(a) }$

$\sf{2. \: \: log(ab) = log(a) + log(b) }$

$\displaystyle \sf{3. \: \: log \bigg( \frac{a}{b} \bigg) = log(a) - log(b) }$

$\sf{4. \: \: log_{a}(a) = 1}$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ log_{4}(2) + log_{4}(32) }$

Step 2 of 2 :

Simplify the expression

$\displaystyle \sf{ log_{4}(2) + log_{4}(32) }$

$\displaystyle \sf{ = log_{4}(2 \times 32) }$

$\displaystyle \sf{ = log_{4}(64) }$

$\displaystyle \sf{ = log_{4} ({4}^{3} ) }$

$\displaystyle \sf{ = 3 log_{4} ({4}^{} ) }$

$\displaystyle \sf{ = 3 \times 1 }$

$\displaystyle \sf{ = 3 }$

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