Question

How do you condense $4\ln 2?$

Answer 1

Hint : Logarithms are ways to figure out which exponents we need to multiply into the specific number. Here, using the property of logarithm the change of base, According to the power rule, the log of a power is equal to the power times the log of the base.
$\log {a^N} = N\log a$

Complete step-by-step answer :
Take the given expression: $4\ln 2$
Use the property of the logarithm in the above expression by using the formula
$\log {a^N} = N\log a$
$4\ln 2 = \ln ({2^4})$
Simplify the above expression –
$4\ln 2 = \ln 16$
This is the required solution.
So, the correct answer is “ $4\ln 2 = \ln 16$ ”.

Note : Know the difference between ln and log and apply its properties accordingly. Logarithms are the ways to figure out which exponents we need to multiply into the specific number. Log is defined for the base $10$ and ln is denoted for the base e. “e” is an irrational and transcendental number which can be expressed as $e = 2.71828$ . You can convert ln to log by using the relation such as
$\ln (x) = \log x \div \log (2.71828)$