What is the answer to (x)=log_{0.5}(x-2)+1 ?

The answer to (x)=log_{0.5}(x-2)+1 is x=-(\W_{0}(-0.5ln(0.5))-2ln(0.5))/(ln(0.5))

Solve for x: (x)=log_{0.5}(x-2)+1

The solution is x=-(\W_{0}(-0.5ln(0.5))-2ln(0.5))/(ln(0.5))

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(x) = lo g_{0.5} (x - 2) + 1

x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

Decimal Notation

x = 2.38333 \dots

Solution steps

(x) = lo g_{0.5} (x - 2) + 1

Switch sides

lo g_{0.5} (x - 2) + 1 = x

Move

1

to the right side

lo g_{0.5} (x - 2) = x - 1

f (x) = g (x),

then

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

0. 5^{l o g_{0.5} (x - 2)} = 0. 5^{x - 1}

Simplify

0. 5^{l o g_{0.5} (x - 2)} : x - 2

x - 2 = 0. 5^{x - 1}

Solve

x - 2 = 0. 5^{x - 1} : x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

Verify Solutions:

x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

True

The solution is

x = - \frac{W _{0} ( - 0.5 ln ( 0.5 ) ) - 2 ln ( 0.5 )}{ln ( 0.5 )}

lo g_{3} (5 x - 3) = 5

lo g_{2} (x + 20) = lo g_{2} (2)

lo g_{2} (2 x) + lo g_{2} (x + 2) = 3

7 lo g_{10} (u) = 1

ln (x^{2}) + 2 x - 5 = 0

What is the answer to (x)=log_{0.5}(x-2)+1 ?
The answer to (x)=log_{0.5}(x-2)+1 is x=-(\W_{0}(-0.5ln(0.5))-2ln(0.5))/(ln(0.5))
Solve for x: (x)=log_{0.5}(x-2)+1
The solution is x=-(\W_{0}(-0.5ln(0.5))-2ln(0.5))/(ln(0.5))