What is the answer to 3ln(7x-1)+4=7 ?

The answer to 3ln(7x-1)+4=7 is x=(e+1)/7

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3ln(7x-1)+4=7

3 ln (7 x - 1) + 4 = 7

x = \frac{e + 1}{7}

Decimal Notation

x = 0.53118 \dots

Solution steps

3 ln (7 x - 1) + 4 = 7

Move

4

to the right side

3 ln (7 x - 1) = 3

Divide both sides by

3

ln (7 x - 1) = 1

Apply log rules

7 x - 1 = e

Solve

7 x - 1 = e : x = \frac{e + 1}{7}

x = \frac{e + 1}{7}

Verify Solutions:

x = \frac{e + 1}{7}

True

The solution is

x = \frac{e + 1}{7}

5 lo g_{5} (a) = lo g_{5} (x)

lo g_{10} (x) = 3 - x

2 ln (4 x + 2) - 20 = - 4

ln (5 x - 1) = ln (2) + ln (7)

lo g_{4} (x + 2) - lo g_{4} (x) = 3