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Explain how to solve 4^(x + 3) = 7 (x+3 being an exponent) using the change of base formula. Include the solution for x in your answer—round your answer to the nearest thousandth.

Explain how to solve 4x 3 7 x3 being an exponent using the change of base formula Include the solution for x in your answerround your answer to the nearest thou class=

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facundo3141592

Using natural logarithms properties, we will see that:

x = -1.596

How to solve the equation?

Here we can use the property:

[tex]ln(a^b) = b*ln(a)[/tex]

Now we have the equation:

[tex]4^{x + 3 }= 7[/tex]

If we apply the natural logarithm in both sides, we get:

[tex]ln(4^{x + 3 })= ln(7)\\\\(x + 3)*ln(4) = ln(7)\\\\x + 3 = ln(7)/ln(4)\\\\x = ln(7)/ln(4) - 3 = log_4(7) - 3 = -1.596[/tex]

If you want to learn more about natural logarithms:

https://brainly.com/question/13473114

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