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Algebra
Question

If $$v = m ^ { ( 6 - \frac { n } { r } ) } ,$$ express $$n$$ in terms of $$r , m$$ and $$v$$ by taking logarithms to base $$10 .$$

$$n = \frac { r } { \log m } ( 6 - \log v )$$

$$n = r \log m ( \log v - 6 \log m )$$

$$n = r ( 6 - \frac { \log v } { \log m } )$$

$$n = \frac { 1 } { m } ( 6 m r - r v )$$

solve for $$n , v = m ( 6 - \frac { n } { r } ) : n = - \frac { r \ln ( v ) - 6 r \ln ( m ) } { \ln ( m ) }$$