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

The answer to ln(3x+1)-ln(4-x)=ln(4) is x= 15/7

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

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

x = \frac{15}{7}

Decimal Notation

x = 2.14285 \dots

Solution steps

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

Add

ln (4 - x)

to both sides

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

Simplify

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

Apply log rules

3 x + 1 = 4 (4 - x)

Solve

3 x + 1 = 4 (4 - x) : x = \frac{15}{7}

x = \frac{15}{7}

Verify Solutions:

x = \frac{15}{7}

True

The solution is

x = \frac{15}{7}

lo g_{2} (x - 2) + 2 = lo g_{2} (32)

lo g_{0.3} (x) = 3

ln (x^{2} + 5 x) = 2 ln (x + 1)

lo g_{6} (x) + lo g_{6} (3) = 2

lo g_{10} (z - 3) = 2

What is the answer to ln(3x+1)-ln(4-x)=ln(4) ?
The answer to ln(3x+1)-ln(4-x)=ln(4) is x= 15/7
Solve for x: ln(3x+1)-ln(4-x)=ln(4)
The solution is x= 15/7