Textbook Question
n Exercises 92–93, rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places. y = 6.5(0.43)^x
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6. Exponential & Logarithmic Functions
Solving Exponential and Logarithmic Equations
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Solve the exponential equation.
A
2
B
5
C
9
D
– 5
Verified step by step guidance1
First, recognize that the equation is in the form of an exponential equation: \( 4^{x+7} = 16 \).
Notice that 16 can be rewritten as a power of 4, since \( 16 = 4^2 \).
Substitute \( 16 \) with \( 4^2 \) in the equation, resulting in \( 4^{x+7} = 4^2 \).
Since the bases are the same, you can set the exponents equal to each other: \( x + 7 = 2 \).
Solve for \( x \) by subtracting 7 from both sides of the equation: \( x = 2 - 7 \).
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