Question

explore the limitations of the values of b and x in equations of the form log_b x = l by determining which logarithm is undefined. (1 point)
log_2.5 6.25
log_1/3 1/9
log_6 1
log_5 0

Explanation:

Step1: Recall logarithm definition

The logarithm $\log_{b}x$ is defined for $b> 0,b
eq1$ and $x > 0$.

Step2: Analyze each option

• For $\log_{2.5}6.25$, $b = 2.5>0,b

eq1$ and $x = 6.25>0$, so it is defined.

• For $\log_{\frac{1}{3}}\frac{1}{9}$, $b=\frac{1}{3}>0,b

eq1$ and $x=\frac{1}{9}>0$, so it is defined.

• For $\log_{6}1$, $b = 6>0,b

eq1$ and $x = 1>0$, so it is defined.

• For $\log_{5}0$, since the logarithm of zero is undefined (there is no real - number $y$ such that $b^{y}=0$ for $b>0,b

eq1$), this logarithm is undefined.

Answer:

$\log_{5}0$