Given the equation V_m= u(ln m_0-ln m_8)- g t_f I need to solve for m_0 Here is what I have but it looks messy and I feel like there is sometihng wrong or a better way

Haiphongum 2022-09-18 Answered
Homework help to rearrange formula
Given the equation
V m = u ( ln m 0 ln m 8 ) g t f
I need to solve for m 0 Here is what I have but it looks messy and I feel like there is sometihng wrong or a better way
1st attempt
V m = u ( ln m 0 ln m 8 ) g t f V m = u ( ln m 0 ) u ( ln m 8 ) g t f V m = u ( ln m 0 ) u ( ln m 8 ) g t f V m = u ( ln m 0 ) u ( ln m 8 ) g t f u ( ln m 0 ) u ( ln m 8 ) g t f V m = 0 u ( ln m 0 ) u ( ln m 8 ) V m = g t f u ( ln m 0 ) = g t f + u ( ln m 8 ) + V m ln m 0 = ( g t f + u ( ln m 8 ) + V m ) ÷ u e ( g t f + u ( ln m 8 ) + V m ) ÷ u = m 0
2nd attempt - think this looks a little better but still not there yet
V m = u ( ln m 0 m 8 ) g t f V m + g t f = u ( ln m 0 m 8 ) V m + g t f u = ln m 0 m 8 e V m + g t f u = m 0 m 8 m 8 e V m + g t f u = m 0
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Answers (1)

anekesanxl
Answered 2022-09-19 Author has 12 answers
Hint:
ln ( a ) ln ( b ) = ln ( a b )

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