What is the answer to (5^{x+1}-20)/(10+5^x)=3 ?

The answer to (5^{x+1}-20)/(10+5^x)=3 is x=2

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(5^{x+1}-20)/(10+5^x)=3

\frac{5 ^{x + 1} - 20}{10 + 5 ^{x}} = 3

x = 2

Solution steps

\frac{5 ^{x + 1} - 20}{10 + 5 ^{x}} = 3

Multiply both sides by

10 + 5^{x}

\frac{5 ^{x + 1} - 20}{10 + 5 ^{x}} (10 + 5^{x}) = 3 (10 + 5^{x})

Simplify

5^{x + 1} - 20 = 3 (10 + 5^{x})

Subtract

3 (10 + 5^{x})

from both sides

5^{x + 1} - 20 - 3 (10 + 5^{x}) = 3 (10 + 5^{x}) - 3 (10 + 5^{x})

Simplify

5^{x + 1} - 20 - 3 (10 + 5^{x}) = 0

Factor

5^{x + 1} - 20 - 3 (10 + 5^{x}) : 2 (5^{x} - 25)

2 (5^{x} - 25) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5^{x} - 25 = 0

Solve

5^{x} - 25 = 0 : x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

10 + 2 \cdot 2^{x} = 18

5^{x} = - x + 6

2 - e^{x} = 0

67 = 1 5^{x}

(3)^{x} = 81

What is the answer to (5^{x+1}-20)/(10+5^x)=3 ?
The answer to (5^{x+1}-20)/(10+5^x)=3 is x=2
Solve for x: (5^{x+1}-20)/(10+5^x)=3
The solution is x=2