Chapter 6.3, Problem 65E

To determine

Check whether all the logarithmic function passes through the point $\left(1,0\right)$ or not.

Answer to Problem 65E

The statement is not correct.

Explanation of Solution

Given information:

The given statement is “ every logarithmic function will pass through the point $\left(1,0\right)$ .”

Formula Used:

Logarithmic power rule is

If ${\log }_{b}p=q$ is a logarithmic expression then the exponential function will be equal $b^q=p$ .

Consider the logarithm expression ${\log }_{b}y=x$ , here $b$ is the base of the log function and $\left(x,y\right)$ is a point on the curve.

Convert into the exponential form. Use the logarithmic power rule.

  $\begin{array}{c}{\log }_{b}y=x\\ b^x=y\end{array}$

Substitute the given point $\left(1,0\right)$ for $\left(x,y\right)$ .

  $\begin{array}{c}{b}^x=y\\ b^1=0\end{array}$

But for the equality of the above condition $b$ must be equal to 0.

Hence, the statement is not correct.