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Popular >

(100e^x)/(e^x+2)=50

Solution

\frac{100 e ^{x}}{e ^{x} + 2} = 50

Solution

x = ln (2)

+1

Decimal Notation

x = 0.69314 \dots

Solution steps

\frac{100 e ^{x}}{e ^{x} + 2} = 50

Multiply both sides by

e^{x} + 2

\frac{100 e ^{x}}{e ^{x} + 2} (e^{x} + 2) = 50 (e^{x} + 2)

Simplify

100 e^{x} = 50 (e^{x} + 2)

Expand

50 (e^{x} + 2) : 50 e^{x} + 100

100 e^{x} = 50 e^{x} + 100

Move

50 e^{x}

to the left side

50 e^{x} = 100

Divide both sides by

50

e^{x} = 2

Apply exponent rules

x = ln (2)

Verify Solutions:

x = ln (2)

True

The solution is

x = ln (2)

Popular Examples

25 \cdot 9 0^{n} = 60 \cdot 6^{n}

3^{2x}-3^x-30=0

3^{2 x} - 3^{x} - 30 = 0

3^{3x}-3^{2x+1}-3^x+3=0

3^{3 x} - 3^{2 x + 1} - 3^{x} + 3 = 0

7^{x} = 6^{x + 7}

7^{2+x}= 1/(49^{x+3)}

7^{2 + x} = \frac{1}{4 9 ^{x + 3}}

Frequently Asked Questions (FAQ)

What is the answer to (100e^x)/(e^x+2)=50 ?
The answer to (100e^x)/(e^x+2)=50 is x=ln(2)