What is the answer to 4/(10^{(x-1))-9}=22 ?

The answer to 4/(10^{(x-1))-9}=22 is x=(ln(101/11))/(ln(10))+1

Solve for x: 4/(10^{(x-1))-9}=22

The solution is x=(ln(101/11))/(ln(10))+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{4}{1 0 ^{(x - 1)} - 9} = 22

x = \frac{ln ( \frac{101}{11} )}{ln ( 10 )} + 1

Decimal

x = 1.96292 \dots

Solution steps

\frac{4}{1 0 ^{(x - 1)} - 9} = 22

Multiply both sides by

1 0^{x - 1} - 9

\frac{4}{1 0 ^{x - 1} - 9} (1 0^{x - 1} - 9) = 22 (1 0^{x - 1} - 9)

Simplify

4 = 22 (1 0^{x - 1} - 9)

Switch sides

22 (1 0^{x - 1} - 9) = 4

Divide both sides by

22

1 0^{x - 1} - 9 = \frac{2}{11}

Move

9

to the right side

1 0^{x - 1} = \frac{101}{11}

Apply exponent rules

(x - 1) ln (10) = ln (\frac{101}{11})

Solve

(x - 1) ln (10) = ln (\frac{101}{11}) : x = \frac{ln ( \frac{101}{11} )}{ln ( 10 )} + 1

x = \frac{ln ( \frac{101}{11} )}{ln ( 10 )} + 1

Verify Solutions:

x = \frac{ln ( \frac{101}{11} )}{ln ( 10 )} + 1

True

The solution is

x = \frac{ln ( \frac{101}{11} )}{ln ( 10 )} + 1

9 \cdot 2^{x} = 6^{x}

x, 1 0^{x + 1} - 1 0^{x} = 3

\frac{2 ^{x} + 2 ^{- x}}{2} = 3

y, 3^{x} + 5^{y} = x^{3} + y

3^{2 x + 1} = 7^{x - 2}

What is the answer to 4/(10^{(x-1))-9}=22 ?
The answer to 4/(10^{(x-1))-9}=22 is x=(ln(101/11))/(ln(10))+1
Solve for x: 4/(10^{(x-1))-9}=22
The solution is x=(ln(101/11))/(ln(10))+1