Exponential and Logarithmic Functions

[thoffman]

First time ever using one of these things, math is starting to catch up with me. I have not taken a math course in 7 years, one of those use it or lose it deals =]. Anyhow, I have two questions.

Condense the expression to the logarithm of a single quantity.

#60) 2 [ln x - ln(x+1) - ln(x -1)]

- I am aware of the properties of logarithm rules but I am totally lost on this question. Assistance from start to finish on this would be great.


Find the exact value of the logarithm without using a calculator. If this is not possible state the reason.

#70) log5(1/125) (the 5 is a subscript)

- Again, I am unsure on this whole problem in general.

Look forward to some insight and assistance. This course is over next week and I need to ensure I at least get a C on the last test =]

Thanks,

Thomas

 

[Deleted member 4993]

First time ever using one of these things, math is starting to catch up with me. I have not taken a math course in 7 years, one of those use it or lose it deals =]. Anyhow, I have two questions.

Condense the expression to the logarithm of a single quantity.

#60) 2 [ln x - ln(x+1) - ln(x -1)]

Use the property of logarithm

Log (A) + Log (B} = Log (AB)

and

C*Log(AB) = Log[(AB)^C]....where '^' indicates 'to the power'
so:

2 [ln x - ln(x+1) - ln(x -1)]

= 2 [ln {x/{(x+1)(x -1)}]

= = ln [{x/(x^2 - 1)}^2]

- I am aware of the properties of logarithm rules but I am totally lost on this question. Assistance from start to finish on this would be great.


Find the exact value of the logarithm without using a calculator. If this is not possible state the reason.

#70) log5(1/125) (the 5 is a subscript)

Use

loga(a^b) = b

so

log5(1/125)

= log5{5^(-3)}

= -3

- Again, I am unsure on this whole problem in general.

Look forward to some insight and assistance. This course is over next week and I need to ensure I at least get a C on the last test =]

Thanks,

Thomas

 

[thoffman]

Thank you for your help.