How to Solve Complex Logarithmic Equations

[zaddyzad]

Homework Statement

A) Solve LogX^(LogX) = 4
B) Log3 X - Log27 X = 4/3

Homework Equations

Basic 3 log rules: 1. Logc(MN) = LogcM + logcN 2. Logc(M/N) = LogcM - LogcN 3. LogcM^p = pLogcM

The Attempt at a Solution

I have no idea how to start either.

 

[symbolipoint]

Find the "Relevant equations" for part 2 of the format.

What is or are the bases for question #B ? Also, what is or are the bases for #A?

Take care of those, and helping you will be easier; otherwise your problem description and question are not understandable.

Homework Statement

A) Solve LogX^(LogX) = 4
B) Log3 X - Log27 X = 4/3

Homework Equations

The Attempt at a Solution

I have no idea how to start either.

 

[zaddyzad]

Find the "Relevant equations" for part 2 of the format.

What is or are the bases for question #B ? Also, what is or are the bases for #A?

Take care of those, and helping you will be easier; otherwise your problem description and question are not understandable.

For part A) the base is 10, therefor that's why it isn't written, and for B it's the 3 and 27.

 

[symbolipoint]

You still need to decide which relevant equations or properties you need for part 2 of the format template. One of them should be the change of base formula for question #B.

 

[zaddyzad]

Those are the only log formulas I know and have learned. This is an extend question.

 

[MarneMath]

If you have a log(x)^(anything) what do you get?

 

[ehild]

You know the relation following from definition of logarithm:
$$a ^{log_a(x)}=x$$

Apply to the base 27 logarithm:

$$27 ^{log_{27}(x)}=x$$Take the base 3 logarithm of both sides: you find how log₂₇(x) is related to log₃(x).

ehild

 

[SammyS]

Homework Statement

A) Solve LogX^(LogX) = 4
B) Log3 X - Log27 X = 4/3

Homework Equations

Basic 3 log rules: 1. Logc(MN) = LogcM + logcN 2. Logc(M/N) = LogcM - LogcN 3. LogcM^p = pLogcM

The Attempt at a Solution

I have no idea how to start either.

I assume that A) is:

Solve $\displaystyle \log\left(x^{\log(x)}\right)=4\ ,\ \$ of course that is a base 10 logarithm, as you noted elsewhere.​

Use the $\displaystyle \log_{\,c}\left(x^{p}\right)=p\,\log_{\,c}(x)\ \$ property on A).

Have you learned the change of base formula? Use it for B).

 

[Saitama]

There is one more property that you can make use of here,
$$log_{a^c} b=\frac{log_a b}{c}$$