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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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In summary: Change of base formula)In summary, the conversation discusses using the laws of logarithms to simplify an equation involving logarithmic expressions. The first step is to transform the equation using the laws of logarithms, and then simplify it using algebraic techniques. The final goal is to get an equation in the form of ##\log_a x = \log_a y##, which can be solved by taking the base to the power of both sides. The conversation also mentions the change of base formula, which can be used to convert logarithms to different bases.
I started off by using law of logs to divide the logb (6x/18) but i dont know what to do after, please help.
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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/
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homeworkhelpls
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i mean i did transform the equation but after idk how to go onfresh_42 said:
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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:
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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) .
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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}##
FAQ: What Is the Next Step in Solving This Logarithmic Equation?
How do I isolate the logarithmic term in the equation?
To isolate the logarithmic term, you need to move all other terms to the opposite side of the equation. This often involves using algebraic operations such as addition, subtraction, multiplication, or division. For example, if you have an equation like \( \log(x) + 3 = 7 \), you would subtract 3 from both sides to get \( \log(x) = 4 \).
What should I do if the equation has multiple logarithmic terms?
If the equation has multiple logarithmic terms, you should try to combine them using logarithmic properties. For example, if you have \( \log(x) + \log(y) = \log(10) \), you can combine the logarithms on the left side using the product rule to get \( \log(xy) = \log(10) \). This simplifies the equation and makes it easier to solve.
How do I remove the logarithm to solve for the variable?
To remove the logarithm, you can exponentiate both sides of the equation by raising the base of the logarithm to the power of both sides. For example, if you have \( \log(x) = 4 \) and the base is 10 (common logarithm), you would rewrite this as \( 10^{\log(x)} = 10^4 \), which simplifies to \( x = 10^4 \).
What if the logarithmic equation involves different bases?
If the logarithmic equation involves different bases, you can use the change of base formula to rewrite the logarithms with a common base. The change of base formula is \( \log_b(a) = \frac{\log_c(a)}{\log_c(b)} \), where \( c \) is the new base you choose. This allows you to work with a single base and simplify the equation.
How do I check for extraneous solutions in a logarithmic equation?
After solving the logarithmic equation, you should substitute your solutions back into the original equation to verify that they are valid. Logarithmic functions have restrictions, such as the argument of the logarithm must be positive. If any solution does not satisfy these conditions, it is considered extraneous and should be discarded.