Asked by Jattiya Arrianna on May 17, 2024
Verified
Solve the exponential equation. Round your answer to two decimal places. 7x+3−5=187 ^ { x + 3 } - 5 = 187x+3−5=18
A) x= -0.77
B) x=−1.64x = - 1.64x=−1.64
C) x=−1.39x = - 1.39x=−1.39
D) x=3.49x = 3.49x=3.49
E) x=−0.69x = - 0.69x=−0.69
Exponential Equation
An equation where the variable appears in the exponent, expressing the relationship between two quantities where one varies as a constant power of another.
Decimal Places
The count of numbers present after the decimal point in a decimal numeral.
- Resolve equations involving exponential functions and comprehend their practical applications.
Verified Answer
RR
Randa RegesMay 18, 2024
Final Answer :
C
Explanation :
To solve for x, we can start by isolating the exponential term:
7x+3=237 ^ { x + 3 } = 237x+3=23
Then, take the logarithm of both sides with base 7:
(x+3)log7(7)=log7(23)(x+3)\log_7(7)=\log_7(23)(x+3)log7(7)=log7(23)
Simplifying,
x+3=log7(23)log7(7)x+3=\frac{\log_7(23)}{\log_7(7)}x+3=log7(7)log7(23)
x+3=log7(23)x+3=\log_{7}(23)x+3=log7(23)
x=log7(23)−3x=\log_{7}(23)-3x=log7(23)−3
Using a calculator, we get:
x≈−1.39x\approx -1.39x≈−1.39
Therefore the answer is C).
7x+3=237 ^ { x + 3 } = 237x+3=23
Then, take the logarithm of both sides with base 7:
(x+3)log7(7)=log7(23)(x+3)\log_7(7)=\log_7(23)(x+3)log7(7)=log7(23)
Simplifying,
x+3=log7(23)log7(7)x+3=\frac{\log_7(23)}{\log_7(7)}x+3=log7(7)log7(23)
x+3=log7(23)x+3=\log_{7}(23)x+3=log7(23)
x=log7(23)−3x=\log_{7}(23)-3x=log7(23)−3
Using a calculator, we get:
x≈−1.39x\approx -1.39x≈−1.39
Therefore the answer is C).
Learning Objectives
- Resolve equations involving exponential functions and comprehend their practical applications.