What is the answer to ln(x+31)-ln(4-3x)=5ln(2) ?

The answer to ln(x+31)-ln(4-3x)=5ln(2) is x=1

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ln(x+31)-ln(4-3x)=5ln(2)

ln (x + 31) - ln (4 - 3 x) = 5 ln (2)

x = 1

Solution steps

ln (x + 31) - ln (4 - 3 x) = 5 ln (2)

Add

ln (4 - 3 x)

to both sides

ln (x + 31) - ln (4 - 3 x) + ln (4 - 3 x) = 5 ln (2) + ln (4 - 3 x)

Simplify

ln (x + 31) = 5 ln (2) + ln (4 - 3 x)

Apply log rules

x + 31 = 32 (4 - 3 x)

Solve

x + 31 = 32 (4 - 3 x) : x = 1

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

lo g_{10} (x) = 1.3

lo g_{x} (216) = 3

lo g_{7} (2 x - 1) = 2

6 lo g_{4} (x + 19) = 12

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

What is the answer to ln(x+31)-ln(4-3x)=5ln(2) ?
The answer to ln(x+31)-ln(4-3x)=5ln(2) is x=1
Solve for x: ln(x+31)-ln(4-3x)=5ln(2)
The solution is x=1