What is the answer to -x+ln(x)0.2x=0 ?

The answer to -x+ln(x)0.2x=0 is x=e^5

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-x+ln(x)0.2x=0

- x + ln (x) 0.2 x = 0

x = e^{5}

Decimal Notation

x = 148.41315 \dots

Solution steps

- x + ln (x) \cdot 0.2 x = 0

Multiply both sides by

10

- 10 x + 2 x ln (x) = 0

Move

10 x

to the right side

2 x ln (x) = 10 x

Move

10 x

to the left side

2 x ln (x) - 10 x = 0

Factor

2 x ln (x) - 10 x : 2 x (ln (x) - 5)

2 x (ln (x) - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or ln (x) - 5 = 0

Solve

ln (x) - 5 = 0 : x = e^{5}

Verify Solutions:

x = 0

False

, x = e^{5}

True

The solution is

x = e^{5}

15 = 25420 + 1581394 \cdot ln (x)

(2 x + 3) ln (5) = 60 (ln (x))

lo g_{2} (x) + 3 = lo g_{2} (x - 7)

lo g_{7 x} (1) = x

x, 0.8 ln (y) = ln (x)