Question

What is the solution of each exponential equation? Check your answer. a. 7⁻⁴x=800

Answer 1

Solution of exponential equation is , x =  $800. 7^4$

What is exponential equation ?

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as  $a^x$ .

where, a = the base of function

           x = main expression

Mathematically, if  $log_aN = x$ is an logarithmic function then, this can be converted to exponential function as  $a^x = N$.

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

Some important formulas of exponential :

• $a^x . a^y = a^{x+y}$
• $\frac{a^x}{a^y} = a^{x-y}$
• $a^x.b^x=(ab)^x$
• $(a^x)^y = a^{xy}$

• $a^{-x} = \frac{1}{a^x}$

According to given statement,

$7^{-4} x = 800$

=> $\frac{1}{7^4} x = 800$

=> $x = 800 . 7^4$

Thus solution for this equation is x =  $800. 7^4$

To know more about exponential equations, visit :

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The complete question is :

What is the solution of each exponential equation? Check your answer.

a. 7⁻⁴x=800

b. 5.2³x=400