Question

Express log 48 in terms of log2 and log3​

Answer 1

$\displaystyle \sf{log \: 48 = 4 \: log \: 2 + log \: 3 }$

Given :

The expression log 48

To find :

To express log 48 in terms of log 2 and log 3

Formula :

We are aware of the formula on logarithm that

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

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

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is log 48

Step 2 of 2 :

Express log 48 in terms of log 2 and log 3

$\displaystyle \sf{ log \: 48}$

$\displaystyle \sf{ = log \: (2 \times 2 \times 2 \times 2 \times 3)}$

$\displaystyle \sf{ = log \: ( {2}^{4} \times 3)}$

$\displaystyle \sf{ = log \: ( {2}^{4} ) +log \: ( 3) }\: \: \: \bigg[ \: \because log(ab) = log(a) + log(b)\: \bigg]$

$\displaystyle \sf{ = 4 \: log \: 2 + log \: 3 }\: \: \: \bigg[ \: \because \: log( {a}^{n} ) = n log(a)\bigg]$

$\displaystyle \sf{ \therefore \: \: log \: 48 = 4 \: log \: 2 + log \: 3 }$

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Answer 2

The express of log 48 is, 4 log2 + log3.

Definition of logarithem:

• Logarithm, the exponent or power to which a base must be raised to yield a given number.

• Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n.

According to the question:

We are aware of the formula on logarithm that:

$1) log(a^{n})= nlog(a)\\\\2) log(ab) = log(a) + log(b)$

Step 1:

Write down the given expression.

Here the given expression is log 48.

Step 2:

Express log 48 in terms of log 2 and log 3.

log 48

= $log(2$×$2$×$2$×$2$×$3$)

=$log(2^{4}$×$3)$

$=4log2 +log3\\\\=log48=4log2+log3$

Hence, 4 log2 + log3 is the log 48 expression.

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