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

The answer to 7ln(3x)+1=3 is x=(e^{2/7})/3

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7ln(3x)+1=3

7 ln (3 x) + 1 = 3

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

Decimal Notation

x = 0.44357 \dots

Solution steps

7 ln (3 x) + 1 = 3

Move

1

to the right side

7 ln (3 x) = 2

Divide both sides by

7

ln (3 x) = \frac{2}{7}

Apply log rules

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

Solve

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

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

Verify Solutions:

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

True

The solution is

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

x^{2 l o g_{10} (x)} = 10 x^{2}

lo g_{2} (x) + lo g_{2} (x - 1) = 1

lo g_{10} (x) + lo g_{10} (x + 9) = 1

lo g_{10} (x) - 1 = 0

y, ln (1 - 2 y) = t