What is the answer to e^{5x}*e^{2x}=200-e^x ?

The answer to e^{5x}*e^{2x}=200-e^x is x=ln(2.12840…)

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e^{5x}*e^{2x}=200-e^x

e^{5 x} \cdot e^{2 x} = 200 - e^{x}

x = ln (2.12840 \dots)

Decimal Notation

x = 0.75537 \dots

Solution steps

e^{5 x} e^{2 x} = 200 - e^{x}

Apply exponent rules

(e^{x})^{7} = 200 - e^{x}

Rewrite the equation with

e^{x} = u

(u)^{7} = 200 - u

Solve

u^{7} = 200 - u : u \approx 2.12840 \dots

u \approx 2.12840 \dots

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 2.12840 \dots : x = ln (2.12840 \dots)

x = ln (2.12840 \dots)

5^{x + 7} = 8

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

3^{x + 2} x 3^{2} = 3^{2 x}

2^{x} + 4^{x} = 2

0.067 = 1 0^{- 15} \cdot 3^{m}

What is the answer to e^{5x}*e^{2x}=200-e^x ?
The answer to e^{5x}*e^{2x}=200-e^x is x=ln(2.12840…)