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

The answer to l(x)=log_{0.5}(x)-1 is x=-(\W(-0.5ln(0.5)l))/(ln(0.5)l)

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l(x)=log_{0.5}(x)-1

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

x = - \frac{W ( - 0.5 ln ( 0.5 ) l )}{ln ( 0.5 ) l}

Solution steps

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

Switch sides

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

Move

1

to the right side

lo g_{0.5} (x) = l x + 1

f (x) = g (x),

then

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

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

Simplify

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

x = 0. 5^{l x + 1}

Solve

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

x = - \frac{W ( - 0.5 ln ( 0.5 ) l )}{ln ( 0.5 ) l}

Verify Solutions:

x = - \frac{W ( - 0.5 ln ( 0.5 ) l )}{ln ( 0.5 ) l}

True

The solution is

x = - \frac{W ( - 0.5 ln ( 0.5 ) l )}{ln ( 0.5 ) l}

lo g_{4} (x^{2} - x + 16) = 2

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

lo g_{x} (3) = 5

2.77 - 1.61 + 0.5 ln (x) - ln (100) = 0

ln (3 x) = 6.4

What is the answer to l(x)=log_{0.5}(x)-1 ?
The answer to l(x)=log_{0.5}(x)-1 is x=-(\W(-0.5ln(0.5)l))/(ln(0.5)l)