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Find the exact solution to ln(2y+5) = 2 + ln(4-y)

Solution is y = 4e² - 5 /2+e²
By applying log laws we can reach the following:
ln(2y+5/4-y) = 2
Given that ln x = log _ex :e² = 2y+5/4-y
Solve linearly :
2y+5 = e²(4-y)
2y+5 = 4e² - ye²
2y + ye²= 4e² -5
y(2 + e²) = 4e² - 5
y = 4e² - 5 /2+e²

Answered by Michael H. • Maths tutor

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