What is the answer to 3.2=ln(x/5) ?

The answer to 3.2=ln(x/5) is x=e^{3.2}*5

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3.2=ln(x/5)

3.2 = ln (\frac{x}{5})

x = e^{3.2} \cdot 5

Decimal Notation

x = 122.66265 \dots

Solution steps

3.2 = ln (\frac{x}{5})

Apply log rules

e^{3.2} = \frac{x}{5}

Multiply both sides by

5

e^{3.2} \cdot 5 = \frac{x}{5} \cdot 5

Simplify

e^{3.2} \cdot 5 = x

Switch sides

x = e^{3.2} \cdot 5

Verify Solutions:

x = e^{3.2} \cdot 5

True

The solution is

x = e^{3.2} \cdot 5

lo g_{10} (x) - lo g_{10} (x - 3) = 1

y^{l o g_{10} (y)} = 100 y

0.84 = lo g_{10} (x)

lo g_{x} (81) = 3

ln (x^{3}) = 18