What is the answer to ln(m)(4)+8ln(4)(m)=6 ?

The answer to ln(m)(4)+8ln(4)(m)=6 is m=(\W_{0}(4e^{3/2}ln(2)))/(4ln(2))

Solve for m: ln(m)(4)+8ln(4)(m)=6

The solution is m=(\W_{0}(4e^{3/2}ln(2)))/(4ln(2))

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ln (m) (4) + 8 ln (4) (m) = 6

m = \frac{W _{0} ( 4 e ^{\frac{3}{2}} ln ( 2 ) )}{4 ln ( 2 )}

Decimal Notation

m = 0.68007 \dots

Solution steps

ln (m) (4) + 8 ln (4) (m) = 6

Move

8 ln (4) m

to the right side

ln (m) \cdot 4 = 6 - 8 ln (4) m

Divide both sides by

4

ln (m) = \frac{3 - 4 m ln ( 4 )}{2}

Apply log rules

ln (m) = \frac{3 - 8 ln ( 2 ) m}{2}

f (x) = g (x),

then

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

e^{l n (m)} = e^{\frac{3 - 8 l n ( 2 ) m}{2}}

Simplify

e^{l n (m)} : m

Simplify

e^{\frac{3 - 8 l n ( 2 ) m}{2}} : e^{\frac{3}{2}} \cdot 1 6^{- m}

m = e^{\frac{3}{2}} \cdot 1 6^{- m}

Solve

m = e^{\frac{3}{2}} \cdot 1 6^{- m} : m = \frac{W _{0} ( 4 e ^{\frac{3}{2}} ln ( 2 ) )}{4 ln ( 2 )}

m = \frac{W _{0} ( 4 e ^{\frac{3}{2}} ln ( 2 ) )}{4 ln ( 2 )}

Verify Solutions:

m = \frac{W _{0} ( 4 e ^{\frac{3}{2}} ln ( 2 ) )}{4 ln ( 2 )}

True

The solution is

m = \frac{W _{0} ( 4 e ^{\frac{3}{2}} ln ( 2 ) )}{4 ln ( 2 )}

lo g_{10} (2 x) + 4 = 1

\frac{( 1 + ln ( x ) )}{x} = 0

ln (1 + x) = 34

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

lo g_{5} (x) = \frac{1}{5}

What is the answer to ln(m)(4)+8ln(4)(m)=6 ?
The answer to ln(m)(4)+8ln(4)(m)=6 is m=(\W_{0}(4e^{3/2}ln(2)))/(4ln(2))
Solve for m: ln(m)(4)+8ln(4)(m)=6
The solution is m=(\W_{0}(4e^{3/2}ln(2)))/(4ln(2))