What is the answer to ((1+7^x))/((1-7^x))=a ?

The answer to ((1+7^x))/((1-7^x))=a is x=(ln(\frac{a-1)/(1+a))}{ln(7)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((1+7^x))/((1-7^x))=a

\frac{( 1 + 7 ^{x} )}{( 1 - 7 ^{x} )} = a

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

Solution steps

\frac{( 1 + 7 ^{x} )}{( 1 - 7 ^{x} )} = a

Multiply both sides by

1 - 7^{x}

\frac{1 + 7 ^{x}}{1 - 7 ^{x}} (1 - 7^{x}) = a (1 - 7^{x})

Simplify

1 + 7^{x} = a (1 - 7^{x})

Expand

a (1 - 7^{x}) : a - a \cdot 7^{x}

1 + 7^{x} = a - a \cdot 7^{x}

Move

1

to the right side

7^{x} = a - a \cdot 7^{x} - 1

Move

a 7^{x}

to the left side

7^{x} + a \cdot 7^{x} = a - 1

Factor

7^{x} + a \cdot 7^{x} : 7^{x} (1 + a)

7^{x} (1 + a) = a - 1

Divide both sides by

1 + a

7^{x} = \frac{a - 1}{1 + a}

Apply exponent rules

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

Solve

x ln (7) = ln (\frac{a - 1}{1 + a}) : x = \frac{ln ( \frac{a - 1}{1 + a} )}{ln ( 7 )}

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

Verify Solutions:

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

True

The solution is

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

4^{x} - 2^{x} = 12

5^{x} = 625

x + e^{x} = 0

(2^{x + 1})^{2} = 64

2^{x - 2} = \frac{512}{( 2 ^{x - 3} )}

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