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

The answer to 2log_{10}(x-2)=4-x is x=(2\W_{0}(5ln(10)))/(ln(10))+2

Solve for x: 2log_{10}(x-2)=4-x

The solution is x=(2\W_{0}(5ln(10)))/(ln(10))+2

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

x = \frac{2 W _{0} ( 5 ln ( 10 ) )}{ln ( 10 )} + 2

Decimal Notation

x = 3.59466 \dots

Solution steps

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

Divide both sides by

2

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

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

1 0^{l o g_{10} (x - 2)} = 1 0^{\frac{4 - x}{2}}

Simplify

1 0^{l o g_{10} (x - 2)} : x - 2

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

Solve

x - 2 = 1 0^{\frac{4 - x}{2}} : x = \frac{2 W _{0} ( 5 ln ( 10 ) )}{ln ( 10 )} + 2

x = \frac{2 W _{0} ( 5 ln ( 10 ) )}{ln ( 10 )} + 2

Verify Solutions:

x = \frac{2 W _{0} ( 5 ln ( 10 ) )}{ln ( 10 )} + 2

True

The solution is

x = \frac{2 W _{0} ( 5 ln ( 10 ) )}{ln ( 10 )} + 2

0.25 = ln (y)

lo g_{4} (x) = - 0.5

lo g_{4} (x - 12) + lo g_{4} (x) = 3

lo g_{2} (2 x + 10) = 5

lo g_{6} (4 x + 5) = 3

What is the answer to 2log_{10}(x-2)=4-x ?
The answer to 2log_{10}(x-2)=4-x is x=(2\W_{0}(5ln(10)))/(ln(10))+2
Solve for x: 2log_{10}(x-2)=4-x
The solution is x=(2\W_{0}(5ln(10)))/(ln(10))+2