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7.1 — Solving Exponential Equations
Question 1
Solve: \( 3^x = 81 \). What is \( x \)?
Solution:
\( 3^x = 81 = 3^4 \), so \( x = 4 \).
Question 2
To solve \( 4^x = 7 \), which approach is correct?
Solution:
Take log of both sides: \( x \log 4 = \log 7 \), so \( x = \frac{\log 7}{\log 4} \approx 1.404 \).
7.2 — Solving Logarithmic Equations
Question 3
Solve: \( \log_2(x) = 5 \). What is \( x \)?
Solution:
Convert to exponential form: \( x = 2^5 = 32 \).
Question 4
Solve: \( \log(3x-1) = 2 \). What is \( x \)? (Round to 1 decimal)