Solve the exponential equation.
Table of contents
- 0. Review of Algebra4h 18m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations1h 43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 5m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 22m
- 10. Combinatorics & Probability1h 45m
6. Exponential & Logarithmic Functions
Solving Exponential and Logarithmic Equations
Multiple Choice
Solve the logarithmic equation.
log7(6x+13)=2
A
3
B
19.17
C
6
D
No Solution
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Verified step by step guidance1
Start by understanding the given equation: \( \log_7(6x + 13) = 2 \). This means that the logarithm of \(6x + 13\) with base 7 is equal to 2.
Recall the definition of a logarithm: \( \log_b(a) = c \) implies \( b^c = a \). Apply this to the equation: \( 7^2 = 6x + 13 \).
Calculate \( 7^2 \), which is 49, and set up the equation: \( 49 = 6x + 13 \).
To isolate \( x \), subtract 13 from both sides of the equation: \( 49 - 13 = 6x \).
Divide both sides by 6 to solve for \( x \): \( x = \frac{36}{6} \).
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