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2 years ago

Solve the following exponential equations. 2(4^x )+ 4^(x+1 )= 342

Mathematics

1 answer:

Cloud [144]2 years ago

5 0

Answer:

x ≈ 2.91644500708

Step-by-step explanation:

The equation can be simplified to ...

2(4^x) +4(4^x) = 342

6(4^x) = 342

4^x = 57

Taking logarithms, we get ...

x = log₄(57) = log(57)/log(4)

x ≈ 2.91644500708

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The equation

ra1l [238]

<h2>Explanation:</h2>

Let's use a trial and improvement method to find this solution.

Step 1. Let's choose x = 8.5

Substituting into the equation:

$(8.5)^2+ 3(8.5) - 94=0? \\ \\ 72.25+25.5-94=0? \\ \\ 3.75\neq 0$

Step 2. Let's choose x = 8.4

Substituting into the equation:

$(8.4)^2+ 3(8.4) - 94=0? \\ \\ 70.56+25.2-94=0? \\ \\ 1.76\neq 0$

Step 3. Let's choose x = 8.3

Substituting into the equation:

$(8.3)^2+ 3(8.3) - 94=0? \\ \\ 68.89+24.9-94=0? \\ \\ -0.21\neq 0$

Since the sign of the equation changes from positive to negative when evaluating from 8.4 to 8.3, then x = 8.3 seems to be a reasonable value. Finally, the solution to 1 decimal place is:

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