Solving Logarithms Questions - Matt's Attempt

  • Thread starter monkeyhead
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In summary, the conversation is about solving an equation and the individual has provided a potential solution and received feedback on its correctness.
  • #1
monkeyhead
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Just a quick check, I've spend hours trying to crack this. Have I gone the right way about it?

Homework Statement


Solve 5^(x-1)= 4^(1-3x)


Homework Equations





The Attempt at a Solution



(x-1)log5 = log4 (1-3x)

xlog5 - log5 = log4 - 3xlog4

xlog5 + 3xlog4= log4 + log 5

x(log5 + 3log4) = log4 + log 5

x= log4 + log 5/(log5 + 3log4)

= 0.519( 3dp)


Many thanks
Matt
 
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  • #2
Looks correct, and I'm assuming that your actual operation was

[tex]x=\frac{\log 20}{\log{(5\times4^3)}}[/tex]
 
  • #3
I see thanks for the feedback
Matt
 
  • #4
If you have a TI, just store your answer and then plug it back into your original equation and see if L=R.
 

FAQ: Solving Logarithms Questions - Matt's Attempt

What are logarithms and why are they important?

Logarithms are mathematical functions that represent the inverse of exponential functions. They are used to solve equations where the unknown variable is in the exponent. Logarithms are important because they allow us to condense large numbers into more manageable values and provide a way to solve complex equations.

How do you solve logarithms?

To solve a logarithm, you need to use the properties of logarithms, such as the product, quotient, and power rules. You can also convert logarithmic equations into exponential form to solve them. It is also helpful to know the basic properties of logarithms, such as log a base a = 1 and log a base 1 = 0.

What is the difference between natural logarithms and common logarithms?

Natural logarithms, denoted as ln, use the base e (approximately 2.718) while common logarithms, denoted as log, use the base 10. This means that ln(x) represents the power to which e must be raised to equal x, while log(x) represents the power to which 10 must be raised to equal x.

How do you recognize when to use logarithms in a problem?

Logarithms are often used in problems involving exponential growth or decay, compound interest, and solving equations with exponents. They can also be used to simplify large values or to find the unknown exponent in an equation.

What are some common mistakes to avoid when solving logarithms?

Some common mistakes when solving logarithms include forgetting to use the correct logarithmic property, mixing up the base of the logarithm, and forgetting to check for extraneous solutions. It is also important to carefully simplify and check your answer, as logarithmic equations can have multiple solutions.

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