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Write an equation and solve it. Anything goes as long as you address the following points:
a. The equation must start with an 'x' variable in an exponent. B. The equation must require logarithms to solve. C. In the solution you must use the power rule, the product rule and the quotient rule at least once each. D. Explain each step as you solve; which rules are you using and why?
e. What challenges did you face as you were writing your problem? Did you run into any dead ends?

Im having trouble thinking up an equation that uses all three rules. The power rule, the product rule, and the quotient rule. I can create one that uses 2 but i cant quiet imagin 3. Im probably just not thinking about it in the right way but any help would be appreciated.

Sagot :

The equation is  4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)

What is an exponential function?

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where 'a' is a constant and a>1

After following the rules to model the equation.

The equation becomes:

[tex]\rm 4^3^x= 8^{1/x}\times 2^{x+3}[/tex]

After solving, we get:

[tex]2^{6x}= 2^{3/x \ +x+3}[/tex]  (power rule)

Taking log on both sides with base 2

[tex]\rm log_2(2^{6x})= log_2(2^{3/x \ +x+3})[/tex]

After solving, we will get a quadratic equation:

[tex]\rm 5x^2-3x-3 = 0[/tex]

After using quadratic formula, we will get,

[tex]\rm x=\dfrac{3+\sqrt{69}}{10}[/tex] or

[tex]\rm x=\dfrac{3-\sqrt{69}}{10}[/tex]

Thus, the equation is  4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)

Learn more about the exponential function here:

brainly.com/question/11487261

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