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

The first one is the answer, log(x+2)/log4.

That's because the change of base formula is the wanted/current.