Math, asked by sujitharanipatnaik, 11 months ago

Express log 48 in terms of log2 and log3​

Answers

Answered by pulakmath007
0

\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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Answered by jhangir789
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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