Logaritms & e calculation difficulties

[Matbatty-Challenged]

Hello,

I am a first-year college student studying Math and I am having a lot of difficulty understanding logarithms and e calculations. There are two exercise problems from this week’s class that I am struggling with at the moment:

Express y in terms of x for—

• log[subscript]7 y = -2 log[subscript]7(x +2) + log[subscript]73 x
• 
  
• e^y = x – 1
• 
  
• Many thanks for any help offered.

 

[Harry_the_cat]

You have probably been taught the log rules:



Q1. Use the third log rule and then the first log rule to simplify the RHS. Then can you see what to do next?

Q2. Take log (to base e) of both sides.

 

[pka]

Express y in terms of x for—

• log[subscript]7 y = -2 log[subscript]7(x +2) + log[subscript]73 x
• e^y = x – 1
• Many thanks for any help offered.

You should learn how to write questions clearly.
Is it, \(\log_7(y)=-2\log_7(x+2)+\log_7(3x)~?\)
If so then \(\log_7(y)=\log_7((3x)(x+2)^{-2})\)

 

[HallsofIvy]

Now, since logarthm is a one-to-one function, you can remove the logarthms from both sides.

 

[JeffM]

The title of your post suggests one difficulty: neither of these problems is about computation at all: there is nothing to calculate.

Moreover, if you are working with e, just treat e as a variable. When you have a final answer, just leave e alone: that is an exact answer. If you are asked for an answer exact to n decimal places, calculate the final answer exactly and THEN use an approximation of e exact to 4 decimal places. Until you get to calculus, e acts like any real number greater than 1.

 

[Matbatty-Challenged]

You have probably been taught the log rules:
View attachment 27376


Q1. Use the third log rule and then the first log rule to simplify the RHS. Then can you see what to do next?

Q2. Take log (to base e) of both sides.

Hello Harry,

Thanks a lot for your help.

M-C

 

[Matbatty-Challenged]

You should learn how to write questions clearly.
Is it, \(\log_7(y)=-2\log_7(x+2)+\log_7(3x)~?\)
If so then \(\log_7(y)=\log_7((3x)(x+2)^{-2})\)

Hello PKA,

Your tip was a great help.

Many thanks.

M-C