What is the answer to ln(5)=x+ln(x-5)+10 ?

The answer to ln(5)=x+ln(x-5)+10 is x=\W_{0}(5/(e^{15)})+5

Solve for x: ln(5)=x+ln(x-5)+10

The solution is x=\W_{0}(5/(e^{15)})+5

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ln (5) = x + ln (x - 5) + 10

x = W_{0} (\frac{5}{e ^{15}}) + 5

Decimal Notation

x = 5.00000 \dots

Solution steps

ln (5) = x + ln (x - 5) + 10

Switch sides

x + ln (x - 5) + 10 = ln (5)

Move

x

to the right side

ln (x - 5) + 10 = ln (5) - x

Move

10

to the right side

ln (x - 5) = ln (5) - x - 10

f (x) = g (x),

then

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

e^{l n (x - 5)} = e^{l n (5) - x - 10}

Simplify

e^{l n (x - 5)} : x - 5

Simplify

e^{l n (5) - x - 10} : 5 e^{- x - 10}

x - 5 = 5 e^{- x - 10}

Solve

x - 5 = 5 e^{- x - 10} : x = W_{0} (\frac{5}{e ^{15}}) + 5

x = W_{0} (\frac{5}{e ^{15}}) + 5

Verify Solutions:

x = W_{0} (\frac{5}{e ^{15}}) + 5

True

The solution is

x = W_{0} (\frac{5}{e ^{15}}) + 5

0.44 = lo g_{2} (x)

ln (x^{4}) = 12

x, ln (x) = 10

lo g_{e} (a) = - 1

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

What is the answer to ln(5)=x+ln(x-5)+10 ?
The answer to ln(5)=x+ln(x-5)+10 is x=\W_{0}(5/(e^{15)})+5
Solve for x: ln(5)=x+ln(x-5)+10
The solution is x=\W_{0}(5/(e^{15)})+5