Question

Solve this logarithm log8/log2

Answer 1

Given,

an expression log8/log2

To Find,

The value of the given expression.

Solution,

By using the property of log we can write,

log 8 = log 2³ = 3 log 2

Now, simplifying the given expression

3 log 2/ log 2 = 3

Hence, the value of log8/log2 = 3.

Answer 2

$\displaystyle \sf{ \frac{log \: 8}{log \: 2} } = 3$

Given :

The expression

$\displaystyle \sf{ \frac{log \: 8}{log \: 2} }$

To find :

The value of the expression

Formula :

$\displaystyle \sf{ log( {a}^{m} ) = m \: log \: a }$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{log \: 8}{log \: 2} }$

Step 2 of 2 :

Find the value of the expression

We use the formula

$\displaystyle \sf{ log( {a}^{m} ) = m \: log \: a }$

Thus the given expression

$\displaystyle \sf{ = \frac{log \: 8}{log \: 2} }$

$\displaystyle \sf{ = \frac{log \: {2}^{3} }{log \: 2} }$

$\displaystyle \sf{ = \frac{3 \: log \: {2}^{} }{log \: 2} }$

$\displaystyle \sf{ = 3 }$

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