數學 logarithms 唔識

2013-03-28 2:02 am

有請數學高手教我點做呢幾個例題 thank you!

Expand the following using the properties of logarithms and simplify.
ln(x4y3)

Use the properties of logarithms to write the following as a single logarithm.
5 ln(x) + 3 ln(y)

Solve the following equation analytically.
1. 4^9x = 1024^(5 − 3x)
2. 65 + 90e^−0.1t = 75

回答 (1)

螞蟻雄兵

2013-03-28 2:48 am

✔ 最佳答案

Expand the following using the propertiesof logarithms and simplify ln(x4y3)
Sol
ln(x4y3)
=ln(x^4)+ln(y^3)
=4ln｜x｜+3lny

Use the properties of logarithms to write the following as a single logarithm
5 ln(x) + 3 ln(y)
Sol
5 ln(x) + 3 ln(y)
=ln(x^5)+ln(y^3)
=ln(x^5y^3)

Solve the following equation analytically
1. 4^9x = 1024^(5 − 3x)
Sol4^9x = 1024^(5 − 3x)
log(4^9x)=log[1024^(5 − 3x)]
9xlog4=(5－3x)log1024
18xlog2=(5－3x)*10log2
18x=(5－3x)*10
18x=50－30x
48x=50
x=25/24

2. 65+90e^(−0.1t)=75
Sol
65+90e^(−0.1t)=75
90e^(−0.1t)=10
e^(－0.1t)=1/9
e^(0.1t)=9
0.1t=ln9
t=10ln9=20ln3

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