求解 高中數學 27^x=216,64^y=36,求(10/x)+(15/y)=？

27^x=216 ==>3^3x=6^3 ==>3^x=6 ==>6^(1/x)=3 ==>6^(10/x)=3^10

64^y=36 ==>2^6y=6^2 ==>2^3y=6 ==>6^(1/y)=8 ==>6^(15/y)=8^15

6^(10/x)*6^(15/y)=3^10*8^15
==>6^[(10/x)+(15/y)]=3^10*8^15
==>log6^[(10/x)+(15/y)]=log3^10*8^15
==>[(10/x)+(15/y)]*log6=10log3+45log2
==>(10/x)+(15/y)=(10log3+45log2)/(log2+log3)=18.316/0.7781=23.54

Sol
27^x=216
xlog27=log216
3log3x=3log6
1/x=log3/log6
64^y=36
ylog64=log36
6ylog2=2log6
1/y=3log2/log6
10/x+15/y
=10log3/log6+45log2/log6
=10+35log2/log6