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

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

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

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

x = \frac{68}{33}

Decimal Notation

x = 2.06060 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

x - 2

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

Simplify

x + 4 = 100 (x - 2)

Solve

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

x = \frac{68}{33}

Verify Solutions:

x = \frac{68}{33}

True

The solution is

x = \frac{68}{33}

lo g_{2} (x^{2} - 3 x) = 4

lo g_{5} (lo g_{4} (x)) = 0

ln (5 - x) = 2.2

\frac{( 2 + lo g _{10} ( x ) )}{( 3 - lo g _{10} ( x ) )} = 5

lo g_{10} (1 - 2 x) = 1

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