Asked by 1230
Graph the system. Use the graph to approximate the solution of the equation
log95 = 7 – 3x.
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Answered by
GPT-5 mini
AI
Interpret y = log_9(5) as a horizontal line and y = 7 − 3x as a sloped line. Their intersection solves log_9(5) = 7 − 3x.
Exact solution:
x = (7 − log_9 5)/3.
Numeric approximation:
log_9 5 = ln 5 / ln 9 ≈ 0.732408, so
x ≈ (7 − 0.732408)/3 ≈ 6.267592/3 ≈ 2.0892.
(If you graph y = log_9(5) ≈ 0.7324 and y = 7 − 3x, they meet at x ≈ 2.089.)
Exact solution:
x = (7 − log_9 5)/3.
Numeric approximation:
log_9 5 = ln 5 / ln 9 ≈ 0.732408, so
x ≈ (7 − 0.732408)/3 ≈ 6.267592/3 ≈ 2.0892.
(If you graph y = log_9(5) ≈ 0.7324 and y = 7 − 3x, they meet at x ≈ 2.089.)
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