What is the answer to ln(x/5)+1=0 ?

The answer to ln(x/5)+1=0 is x= 5/e

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ln(x/5)+1=0

ln (\frac{x}{5}) + 1 = 0

x = \frac{5}{e}

Decimal

x = 1.83939 \dots

Solution steps

ln (\frac{x}{5}) + 1 = 0

Move

1

to the right side

ln (\frac{x}{5}) = - 1

Apply log rules

\frac{x}{5} = e^{- 1}

Multiply both sides by

5

\frac{x}{5} \cdot 5 = e^{- 1} \cdot 5

Simplify

e^{- 1} \cdot 5 : \frac{5}{e}

x = \frac{5}{e}

Verify Solutions:

x = \frac{5}{e}

True

The solution is

x = \frac{5}{e}

lo g_{10} (x) + lo g_{10} (x + 2) = 1

lo g_{2} (10 + 3 x) = 5

lo g_{2} (1 + x) = 6

y, ln (y) = x

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