If log x - 2m - 3n and log y - 3n - 2m- then the value of log x3- y2 in terms of m and n is

If the sums of n terms of two arithmetic progressions are in the ratio 3n+5:5n-7, then their n^th terms are in the ratio
(a) 3n-15:n-1
(b) 3n+15:n+1
(c) 5n+13:n+1
(d) 5n-13:n-1

Q. If

\frac{log x}{l + m - 2 n} = \frac{log y}{m + n - 2 l} = \frac{log z}{n + l - 2 m}

, then the value of

x^{2} y^{2} z^{2}

will be

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If logx=2m−3n and logy=3n−2m, then the value of log(x3÷y2) in terms of m and n is

The correct option is D 10m−15nlogx=2m−3nlogy=3n−2mlog(x3y2)=logx3−logy2=3logx−2logy=3(2m−3n)−2(3n−2m)=6m−9n−6n+4m=10m−15n

If $log x = 2 m - 3 n$ and $log y = 3 n - 2 m$ , then the value of $log (x^{3} \div y^{2})$ in terms of $m$ and $n$ is

The correct option is D $10 m - 15 n$
$log x = 2 m - 3 n log y = 3 n - 2 m log (\frac{x^{3}}{y^{2}}) = log x^{3} - log y^{2} = 3 log x - 2 log y = 3 (2 m - 3 n) - 2 (3 n - 2 m) = 6 m - 9 n - 6 n + 4 m = 10 m - 15 n$