Find the limit of 5log(x) as x approaches 1

 Exercise

$\lim_{x\to1}5logx$

 

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

$\lim_{x\to1}\left(\frac{5\ln\left(x\right)}{\ln\left(10\right)}\right)$

 

Evaluate the limit $\lim_{x\to1}\left(\frac{5\ln\left(x\right)}{\ln\left(10\right)}\right)$ by replacing all occurrences of $x$ by $1$

$\frac{5\ln\left(1\right)}{\ln\left(10\right)}$

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Calculating the natural logarithm of $1$

$\frac{5\cdot 0}{\ln\left(10\right)}$

 

Multiply $5$ times $0$

$\frac{0}{\ln\left(10\right)}$

 

Zero divided by anything is equal to zero

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