- #1
homeworkhelpls
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I started off by using law of logs to divide the logb (6x/18) but i dont know what to do after, please help.
What Is the Next Step in Solving This Logarithmic Equation?
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Homework Help Overview
The discussion revolves around solving a logarithmic equation involving the transformation of logarithmic expressions and the application of logarithmic properties. Participants are exploring the steps necessary to simplify and solve the equation.
Discussion Character
- Exploratory, Mathematical reasoning, Assumption checking
Approaches and Questions Raised
- Participants discuss the transformation of logarithmic expressions and question the next steps after applying logarithmic laws. There are suggestions to merge terms and utilize properties of logarithms to progress in solving the equation.
Discussion Status
The discussion is active with participants providing guidance on how to proceed with the logarithmic equation. Some participants are questioning the original poster's reasoning and suggesting further transformations, indicating a collaborative effort to clarify the problem.
Contextual Notes
There are references to specific conditions for the logarithmic properties to hold, such as the positivity of variables involved. Additionally, there is a mention of how to format mathematical expressions within the forum.
I started off by using law of logs to divide the logb (6x/18) but i dont know what to do after, please help.
- #2
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If you have transformed ##\log(6x)-\log(18)## to ##\log(6x/18)## then why did you stop? Put in ##x-1## as well.homeworkhelpls said:
Btw.: Here is explained how you can type formulas on PF: https://www.physicsforums.com/help/latexhelp/
- #3
homeworkhelpls
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i mean i did transform the equation but after idk how to go onfresh_42 said:
- #4
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Merge ##\log\left(\dfrac{6x}{18}\right)+\log(x-1)##. Then you get an equation ##\log \ldots = \log \ldots## which you can take ##b## to the power of it.homeworkhelpls said:
- #5
symbolipoint
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All terms are to the same base b. Properly using the logarithm properties and some simplifications should bring you to a step showing 3(x+4)=2x(x-1) .
- #6
mcastillo356
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Laws of Logarithms
If ##x>0##, ##y>0##, ##a>0##, ##b>0##, ##a\neq 1##, and ##b\neq 1##, then
(i) ##\log_a 1=0##
(iii)##\log_a {(xy)}=\log_a x+\log_a y##
(iii)##\log_a {\left(\dfrac{1}{x}\right)}=-\log_a x##
(iv)##\log_a {\left(\dfrac{x}{y}\right)}=\log_a x-\log_a y##
(v)##\log_a {(x^y)}=y\log_a x##
(vi)##\log_a x=\displaystyle\frac{\log_b x}{\log_b a}##
If ##x>0##, ##y>0##, ##a>0##, ##b>0##, ##a\neq 1##, and ##b\neq 1##, then
(i) ##\log_a 1=0##
(iii)##\log_a {(xy)}=\log_a x+\log_a y##
(iii)##\log_a {\left(\dfrac{1}{x}\right)}=-\log_a x##
(iv)##\log_a {\left(\dfrac{x}{y}\right)}=\log_a x-\log_a y##
(v)##\log_a {(x^y)}=y\log_a x##
(vi)##\log_a x=\displaystyle\frac{\log_b x}{\log_b a}##