Master Logarithmic Equations: Expert Tips for Solving Problems

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  • #1
bluff_boy
3
0
Having problems with these questions, what's putting me off is for example the first question, if the numbers 9 and 5 were the same I think I could do it. Do I have to get them to the same number or do I just multiply them?
 

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  • #2
For (1). Take log of both sides and use logarithm rules.

That's about all the help I'm giving you right now. You make an effort now.
 
  • #3
For (ii), multiply both sides by et. Let w = et, and rewrite the equation in terms of w. What does the resulting equation look like now?
 
  • #4
bluff_boy said:
Having problems with these questions, what's putting me off is for example the first question, if the numbers 9 and 5 were the same I think I could do it. Do I have to get them to the same number or do I just multiply them?

(i) lhs= 125*[9^3 *5^2]^x = 125* 18225^x
rhs = 3^3*2^4/5^2 *[3^4/2/5^3]^x = (432/25)(81/250)^x.
Thus, [18225*250/81]^x = (432/25)/125.

(ii) Put x = exp(t) and see what you get.

(iii) Put x = ln(i+2). First you need to decide if [itex] \ln(i+2)^6 [/itex] means [itex] \ln [(i+2)^6] [/itex] or [itex] [ \ln (i+2) ]^6 . [/itex]

RGV
 

Related to Master Logarithmic Equations: Expert Tips for Solving Problems

1. What are logarithmic equations?

Logarithmic equations are mathematical equations that involve logarithms, which are mathematical functions that express the relationship between two numbers by indicating the power to which a base number must be raised to produce the second number.

2. Why are logarithmic equations important?

Logarithmic equations are important because they are commonly used in many fields of science, such as physics, chemistry, and biology. They are also used in financial modeling, computer science, and other areas of mathematics. Understanding how to solve logarithmic equations is crucial for solving complex problems and making accurate predictions.

3. What are some tips for solving master logarithmic equations?

Some tips for solving master logarithmic equations include identifying the base and exponent, using logarithm properties to simplify the equation, and isolating the variable on one side of the equation. It's also important to check for extraneous solutions and to always double-check your answer.

4. How can I improve my skills in solving logarithmic equations?

To improve your skills in solving logarithmic equations, it's important to practice regularly and familiarize yourself with logarithm properties and rules. You can also seek help from a tutor or attend a workshop or class on logarithmic equations. Additionally, try to understand the real-life applications of logarithmic equations to better grasp their significance.

5. Can logarithmic equations be solved using a calculator?

Yes, logarithmic equations can be solved using a calculator. Most scientific calculators have a logarithm function, which allows you to input the base and exponent and solve the equation. However, it's important to understand the steps involved in solving logarithmic equations by hand to ensure accuracy and avoid errors when using a calculator.

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