Master Logarithmic Functions: Solve Equations with Integers | 3(6x-1) = 1 + 4/6x

In summary, the conversation focused on solving the equation 3(6x-1) = 1 + 4/6x in the form x = a - log6b where a and b are integers. The steps involved in solving the equation were discussed and it was suggested to take logarithms of both sides to simplify the equation. The conversation also touched upon taking breaks while studying and solving equations of the form Ax=B for x.
  • #1
thornluke
37
0

Homework Statement


Solve 3(6x-1) = 1 + 4/6x giving your answer in the form x = a - log6b where a,b are integers (Z)


Homework Equations





The Attempt at a Solution


3(6x)(6-1)(6x) = 6x + 4
Let 6x be y,
(1/2)y2 - y - 4 = 0
y = 1 ± √(1+8) = 1 ± 3
3x = 4
xlog63 = log64

What should I do next? :confused:
 
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  • #2
thornluke said:
3(6x)(6-1)(6x) = 6x + 4
Let 6x be y,
y = 1 ± 3
3x = 4
xlog63 = log64

Read the bolded statements carefully. :wink:
 
  • #3
Infinitum said:
Read the bolded statements carefully. :wink:

OH NO! What is IB HL Maths doing to me :eek:
Thanks! :approve:
 
  • #4
thornluke said:
OH NO! What is IB HL Maths doing to me :eek:
Thanks! :approve:

Its normal, after lots of studying!
Take short breaks, now and then :biggrin:
 
  • #5
Isn't it 6x = 4?
 
  • #6
Yes, now take the logarithm, with respect to any base, of both sides.

By the way, going back to your first formula, [itex]x log_6(3)= log_6(4)[/itex], how would you solve any equation of the form Ax= B for x?
 
  • #7
HallsofIvy said:
Yes, now take the logarithm, with respect to any base, of both sides.

By the way, going back to your first formula, [itex]x log_6(3)= log_6(4)[/itex], how would you solve any equation of the form Ax= B for x?

What do you mean by "form Ax= B for x?" ? :eek:
 

Related to Master Logarithmic Functions: Solve Equations with Integers | 3(6x-1) = 1 + 4/6x

1. What is a logarithmic function?

A logarithmic function is a mathematical function that is defined as the inverse of an exponential function. It is written in the form of y = logb(x), where b is the base and x is the input value.

2. How do you solve equations with logarithmic functions?

To solve an equation with a logarithmic function, you need to use the properties of logarithms to isolate the variable on one side of the equation. This may involve using the power rule, product rule, quotient rule, or change of base formula.

3. What does it mean to solve an equation with integers?

Solving an equation with integers means finding the value of the variable that makes the equation true when only whole numbers (positive, negative, or zero) are used.

4. How do you solve the equation 3(6x-1) = 1 + 4/6x?

To solve this equation, you first need to distribute the 3 on the left side, which gives you 18x - 3 = 1 + 4/6x. Then, you can combine like terms and move all the terms with x to one side of the equation. Finally, you can use the properties of logarithms to isolate the x variable and solve for its value.

5. Can you use a calculator to solve equations with logarithmic functions?

Yes, you can use a calculator to solve equations with logarithmic functions. Most scientific calculators have a log key that allows you to input the base and the argument, and it will give you the logarithm value. However, it is important to understand the steps and properties used to solve the equation manually before relying on a calculator.

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