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What value of x satisfies this equation? 1.5(4)^2x=12 Round your answer to the nearest hundredth. The value of x is ____.

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What value of x satisfies this equation 1542x12 Round your answer to the nearest hundredth The value of x is I already have the answer just putting this on brai class=
What value of x satisfies this equation 1542x12 Round your answer to the nearest hundredth The value of x is I already have the answer just putting this on brai class=

Respuesta :

Answer:

x = 0.75

Step-by-step explanation:

1.5(4)^(2x) = 12

Divide both sides by 1.5

4^(2x) = 8

Take the log of both sides

2x * log4 = log8

Divide both sides by log4

2x = log8 / log4

2x = 1.5

Divideboth sides by 2

x = 0.75

The answer is x = 0.75

What is an equation?

"An equation is a mathematical statement where the value of two algebraic expressions are equal."

Given equation: [tex]1.5(4)^{2x}=12[/tex]

We need to find the value of x.

[tex]1.5(4)^{2x}=12[/tex]

⇒ [tex](4)^{2x}=\frac{12}{1.5}[/tex]                        .......................(Divide each side by 1.5)

⇒ [tex]4^{2x}=8[/tex]                              

⇒ [tex](2^{2} )^{2x}=2^3[/tex]

⇒ [tex]2^{4x}=2^3[/tex]

⇒ [tex]4x=3[/tex]                             ........................(Since base of the power is same)

⇒ [tex]x=\frac{3}{4}[/tex]                               ........................(Divide each side by 4)

⇒ [tex]x=0.75[/tex]

Therefore, the correct answer is x = 0.75

Learn more about equations here:

https://brainly.com/question/13170101

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