Question

Which expression results when the change of base formula is applied to log4(x+2) ?

Answer 1

Answer-

$\frac{\log (x+2)}{\log 4}$ is the correct answer.

Solution-

The formula for change of base in logarithm is given by,

$\log_{b}a=\frac{\log_{c}a}{\log_{c}b}$

If we take the common base as 'e' , the formula becomes,

$\log_{b}a=\frac{\log a}{\log b}$

Applying this formula,

$\log_{4}(x+2)=\frac{\log (x+2)}{\log 4}$

∴ As the first option matches with our answer, hence it is the correct answer.

( In the fourth option a bracket is missing, so it is not the correct option)

Answer 2

Based on the change of base formula, the correct answer would be D. $\frac{Log (x + 2)}{Log 4}$

What is the change of base formula?

When shown without a common base, it is depicted as:

$Log _ b a = \frac{Log a}{Log b}$

With "a" being 4 and "b" being (x + 2), the change of base formula would lead to the expression becoming:

$Log _ 4 (x + 2) = \frac{Log (x + 2)}{Log 4}$

In conclusion, option D is correct.

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