Question

How do you \[\log \left( { - 5x} \right) = 27\] in exponential form ?

Answer 1

Hint:An exponential function is a function of the form \[{a^n}\] in which n is a variable and a is a constant term which is called the base of the function. The given function is in terms of log so we need to convert logarithmic form to exponential form by finding the value of \[x\].

Complete step by step answer:
To find \[\log \left( { - 5x} \right) = 27\]in exponential form,
We need to convert log form to exponent form i.e.,
\[ - 5x = {10^{27}}\]
Hence, to find the value of \[x\], divide both sides of the equation by -5, we get
\[\dfrac{{ - 5x}}{{ - 5}} = \dfrac{{{{10}^{27}}}}{{ - 5}}\]
Simplify the terms to get the value of \[x\], as
\[x = - \dfrac{{{{10}^{27}}}}{5}\]
As we can see that the obtained value of \[x\] is in exponential form, as the numerator term consists of exponent as it is of the form 10 raised to the power of 27.

Additional Information:
A mathematical notation of expressing a quantity as a number raised to the power of another number is called the exponential form and it is also called as exponential notation. Exponential numbers take the form \[{a^n}\], where a is multiplied by itself n times. In exponential notation, a is termed the base while n is termed the power or exponent or index.

The exponential notation helps to express a very large number in the form of a single number and 10 raised to the power of the respective exponent. The power of the exponent can be in two forms. It can be either positive or negative. Positive power denotes the number is large and negative power denotes the number is small. The number of multiplying factors is displayed as a superscript of the number which is considered to split the quantity. This special mathematical notation represents the quantity and it is called exponential form.

Note: When rewriting an exponential equation in log form or a log equation in exponential form, it is helpful to remember that the base of the logarithm is the same as the base of the exponent. Hence to solve this, we need to consider that the given function is in exponential form or logarithmic form, hence based on this we can solve the function.