What is the answer to 3ln(2x-7)=9 ?

The answer to 3ln(2x-7)=9 is x=(e^3+7)/2

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3ln(2x-7)=9

3 ln (2 x - 7) = 9

x = \frac{e ^{3} + 7}{2}

Decimal

x = 13.54276 \dots

Solution steps

3 ln (2 x - 7) = 9

Divide both sides by

3

ln (2 x - 7) = 3

Apply log rules

2 x - 7 = e^{3}

Solve

2 x - 7 = e^{3} : x = \frac{e ^{3} + 7}{2}

x = \frac{e ^{3} + 7}{2}

Verify Solutions:

x = \frac{e ^{3} + 7}{2}

True

The solution is

x = \frac{e ^{3} + 7}{2}

ln (x) = 10

ln (x) + ln (2 x + 1) = 2

lo g_{6} (x^{2} - 5 x) = 2

- 7 + lo g_{3} (4 - x) = - 6

lo g_{10} (x) + lo g_{10} (8) = 2