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Popular >

e^{x+1}=e^x+7

Solution

e^{x + 1} = e^{x} + 7

Solution

x = ln (\frac{7}{e - 1})

+1

Decimal Notation

x = 1.40458 \dots

Solution steps

e^{x + 1} = e^{x} + 7

Subtract

e^{x}

from both sides

e^{x + 1} - e^{x} = e^{x} + 7 - e^{x}

Simplify

e^{x + 1} - e^{x} = 7

Factor

e^{x + 1} - e^{x} : (e - 1) e^{x}

(e - 1) e^{x} = 7

Divide both sides by

e - 1

e^{x} = \frac{7}{e - 1}

Apply exponent rules

x = ln (\frac{7}{e - 1})

Popular Examples

5^{x+1}-5^{x-2}=620

5^{x + 1} - 5^{x - 2} = 620

3^{x+1}-4\times 3^{x-2}=69

3^{x + 1} - 4 \times 3^{x - 2} = 69

(e^x+9)/(e^{-x)+5}=2

\frac{e ^{x} + 9}{e ^{- x} + 5} = 2

4 \cdot 2^{x} = 5

(3^x+3^{-x})/(3^x-3^{-x)}=20

\frac{3 ^{x} + 3 ^{- x}}{3 ^{x} - 3 ^{- x}} = 20

Frequently Asked Questions (FAQ)

What is the answer to e^{x+1}=e^x+7 ?
The answer to e^{x+1}=e^x+7 is x=ln(7/(e-1))