What is the answer to 0=log_{10}((x-2)/(x+4))+2 ?

The answer to 0=log_{10}((x-2)/(x+4))+2 is x= 68/33

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0=log_{10}((x-2)/(x+4))+2

0 = lo g_{10} (\frac{x - 2}{x + 4}) + 2

x = \frac{68}{33}

Decimal Notation

x = 2.06060 \dots

Solution steps

0 = lo g_{10} (\frac{x - 2}{x + 4}) + 2

Switch sides

lo g_{10} (\frac{x - 2}{x + 4}) + 2 = 0

Move

2

to the right side

lo g_{10} (\frac{x - 2}{x + 4}) = - 2

Apply log rules

\frac{x - 2}{x + 4} = 1 0^{- 2}

Multiply both sides by

x + 4

\frac{x - 2}{x + 4} (x + 4) = 1 0^{- 2} (x + 4)

Simplify

1 0^{- 2} (x + 4) : \frac{1}{100} (x + 4)

x - 2 = \frac{1}{100} (x + 4)

Solve

x - 2 = \frac{1}{100} (x + 4) : x = \frac{68}{33}

x = \frac{68}{33}

Verify Solutions:

x = \frac{68}{33}

True

The solution is

x = \frac{68}{33}

3 lo g_{x} (81) = - 12

lo g_{a} (x + 1) = 1 + lo g_{a} (x)

lo g_{4} (5 x - 9) - 2 = 0

lo g_{8} (x + 4) = 2

ln (y) = \frac{1}{2}

What is the answer to 0=log_{10}((x-2)/(x+4))+2 ?
The answer to 0=log_{10}((x-2)/(x+4))+2 is x= 68/33
Solve for x: 0=log_{10}((x-2)/(x+4))+2
The solution is x= 68/33