SOLUTION: Please help this is an emergancy! Solve 125^(9x-2)=150 Solve 1/16=64^(4x-3) Solve log(x+9)-logx=3 Use a graphing calculator solve 5^4x=1720 by grpaing. Round to the neares

Question 253334: Please help this is an emergancy!
Solve 125^(9x-2)=150
Solve 1/16=64^(4x-3)
Solve log(x+9)-logx=3
Use a graphing calculator solve 5^4x=1720 by grpaing. Round to the nearest Hundreth if neccesary.
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Your Answer:
1) Given,
125^(9x-2) = 150
Taking log on both sides,
log[125^(9x-2) = log150
(9x-2)log125 = log150
9xlog125-2log125 = log150
9x log125 = log150 +2log125
9x log 5^3 = log 150+log 125^2
3*9xlog5 = log[150*125^2]
27x log5 = log 2343750
x = ( log 2343750)/27log5
2) 1/16 = 64^(4x-3)
Taking log on both sides,
log[1/16) = log64^(4x-3)
log1-log16 = (4x-3)log64
0-log16 = 4xlog64-3log64
3log64-log16 = 4xlog64
log64^3-log16 = 4xlog2^6
log262144-log16 = 24xlog2
log(262144/16) = 24xlog2
log 16384 = 24xlog2
log 2^14 = 24xlog2
14 log2 = 24xlog2
x =(14log2)/(24log2)
x = 7/12
3) log(x+9)-logx = 3
log[(x+9)/x] = 3
Taking anti-log
(x+3)/x = 10^3
x+3 = 1000x
3 = 999x
1 = 333x
x = 1/333

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