Question

How do you evaluate anti $\ln \left( -0.7831 \right)$ ?

Answer 1

Hint: We know that inverse function of ln x is $anti\ln (x)$ that means if ln x is y then anti ln of y is equal to x. ${{e}^{x}}$ is also inverse function of ln x . So we can say that $anti\ln (x)$ is equal to ${{e}^{x}}$ , So $anti\ln (x)$ is always a positive real number. Now we can find the value of anti $\ln \left( -0.7831 \right)$. We can use antilog table to find the value of anti $\ln \left( -0.7831 \right)$ .

Complete step-by-step answer:
We have to evaluate anti $\ln \left( -0.7831 \right)$ , we know that $anti\ln (x)$ is inverse of ln x
So $anti\ln (x)$ is equal to ${{e}^{x}}$ , we can write anti $\ln \left( -0.7831 \right)$ is equal to ${{e}^{-0.7831}}$
We know the property of exponential function ${{e}^{-x}}$ is equal to $\dfrac{1}{{{e}^{x}}}$
So we can write ${{e}^{-0.7831}}$ is equal to $\dfrac{1}{{{e}^{0.7831}}}$
We can not find it by manually, we can use calculator or log table to find the value of $\dfrac{1}{{{e}^{0.7831}}}$

Note: We know that log and antilog are inverse of each other . Note down some property of antilog, product of antilog of a and antilog of b is equal to antilog of (a + b) . antilog of a divided by antilog of b is equal to antilog of ( a – b ) . Domain of log function is always positive so the range of antilog is always positive. Domain of antilog can be negative numbers. Antilog of 0 is always equal to 1 as we know e to power is equal to 1.