Question

log 16 - log 2 will be equal to

Answer 1

log 16 - log 2
log 2^4/log 2
4log 2/log 2
= 4

Answer is : 4

Answer 2

Answer:

Step-by-step explanation:

The value of log 16 - log 2 is 4.

Quotient Rule

The difference between the logarithms of the numerator and denominator is the logarithm of the ratio of two numbers.

$log(\frac{x}{y} ) = log x - log y$

Power Rule:

The exponent can be moved to the front of the logarithm, according to the logarithm power rule.

$IogY^X= X Iog Y$

Given:

The given expression is $log 16 - log 2$.

To Find:

We need to find the value of  $log 16 - log 2$.

Solution:

$log 16 - log 2 = log 2^4 - log 2$

By using the Quotient Rule,

$log(\frac{x}{y} ) = log x - log y$

⇒ $log 16 - log 2 =\frac{log 16}{log 2}$

⇒$log 16 - log 2 =\frac{log 2^4}{log 2}$

By using the Power Rule,

$IogY^X= X Iog Y$

⇒$log 16 - log 2 =\frac{4log 2}{log 2}$

⇒$log 16 -log 2 = 4$

Therefore, the value of $log 16 -log 2 = 4$.

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