a^m*a^n=4,a^m/a^n=6,求mn的值

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a^m*a^n=4,a^m/a^n=6,求mn的值
a^m*a^n=4,a^m/a^n=6,求mn的值

a^m*a^n=4,a^m/a^n=6,求mn的值
由a^m*a^n=4,a^m/a^n=6得
a^m=2√6,a^n=√6/3
m=3/2*log(a)2+1/2*log(a)3,n=1/2*log(a)2-1/2*log(a)3

两式相乘得a^2m=24,两边取对数2mlna=ln24
m=ln24/2lna
两式相除得a^2n=2/3,两边取对数2nlna=ln(2/3)
n=ln(2/3)/2lna