Find the limit of log2(x+4) as x approaches 4

 Exercise

\lim_{x\to4}\:\log2\left(x+4\right)

 

Change the logarithm to base $e$ applying the change of base formula for logarithms: $\log_b(a)=\frac{\log_x(a)}{\log_x(b)}$

\lim_{x\to4}\left(\frac{\ln\left(x+4\right)}{\ln\left(2\right)}\right)

 

Evaluate the limit $\lim_{x\to4}\left(\frac{\ln\left(x+4\right)}{\ln\left(2\right)}\right)$ by replacing all occurrences of $x$ by $4$

\frac{\ln\left(4+4\right)}{\ln\left(2\right)}

 

Add the values $4$ and $4$

\frac{\ln\left(8\right)}{\ln\left(2\right)}

\frac{\ln\left(8\right)}{\ln\left(2\right)}

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