What is the answer to 2(5^{x+1})=1+3/(5^x) ?

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

Solve for x: 2(5^{x+1})=1+3/(5^x)

The solution is x=(ln(3/5))/(ln(5))

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2 (5^{x + 1}) = 1 + \frac{3}{5 ^{x}}

x = \frac{ln ( \frac{3}{5} )}{ln ( 5 )}

Decimal Notation

x = - 0.31739 \dots

Solution steps

2 (5^{x + 1}) = 1 + \frac{3}{5 ^{x}}

Apply exponent rules

2 \cdot 5^{x} \cdot 5^{1} = 1 + 3 (5^{x})^{- 1}

Rewrite the equation with

5^{x} = u

2 u \cdot 5^{1} = 1 + 3 (u)^{- 1}

Solve

2 u \cdot 5^{1} = 1 + 3 u^{- 1} : u = \frac{3}{5}, u = - \frac{1}{2}

u = \frac{3}{5}, u = - \frac{1}{2}

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = \frac{3}{5} : x = \frac{ln ( \frac{3}{5} )}{ln ( 5 )}

Solve

5^{x} = - \frac{1}{2} :

No Solution for

x \in R

x = \frac{ln ( \frac{3}{5} )}{ln ( 5 )}

Verify Solutions:

x = \frac{ln ( \frac{3}{5} )}{ln ( 5 )}

True

The solution is

x = \frac{ln ( \frac{3}{5} )}{ln ( 5 )}

3^{x} = 33

5 e^{3 x} - 4 = 6

- 2 \times 1 0^{4 x} = - 300

7^{5 x + 3} = 512

4^{d} = 8^{6}

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