What is the answer to 27=(75)/(ln(x+1)) ?

The answer to 27=(75)/(ln(x+1)) is x=e^{25/9}-1

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27=(75)/(ln(x+1))

27 = \frac{75}{ln ( x + 1 )}

x = e^{\frac{25}{9}} - 1

Decimal Notation

x = 15.08324 \dots

Solution steps

27 = \frac{75}{ln ( x + 1 )}

Rewrite the equation with

ln (x + 1) = u

27 = \frac{75}{u}

Solve

27 = \frac{75}{u} : u = \frac{25}{9}

u = \frac{25}{9}

Substitute back

u = ln (x + 1),

solve for

x

Solve

ln (x + 1) = \frac{25}{9} : x = e^{\frac{25}{9}} - 1

x = e^{\frac{25}{9}} - 1

Verify Solutions:

x = e^{\frac{25}{9}} - 1

True

The solution is

x = e^{\frac{25}{9}} - 1

lo g_{8} (x) - lo g_{8} (x - 3) = 2

lo g_{2 x - 3} (3 x^{2} - 18) = 2

4 ln (5 x - 4) - 11 = 5

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

lo g_{3} ((x - 1)^{2}) = 2

What is the answer to 27=(75)/(ln(x+1)) ?
The answer to 27=(75)/(ln(x+1)) is x=e^{25/9}-1
Solve for x: 27=(75)/(ln(x+1))
The solution is x=e^{25/9}-1