Solve Logarithmic Equation: 7(3+7x)-3(4-2x)=0

  • MHB
  • Thread starter datafiend
  • Start date
  • Tags
    Logarithmic
In summary, a logarithmic equation is an equation where the variable appears in the exponent and can be solved using logarithms. To solve a logarithmic equation, you can use the properties of logarithms and basic algebra to isolate the variable. The properties of logarithms include the product rule, quotient rule, power rule, and logarithmic identities. If a logarithmic equation has a negative number inside the logarithm or an answer that makes the base equal to 0, it has no solutions. You can check your solution by plugging it back into the original equation.
  • #1
datafiend
31
0
i have the equation 7(3+7x) = 3(4-2x)

so, I tried 7(3+7x)-3(4-2x)=0

...
 
Mathematics news on Phys.org
  • #2
datafiend said:
i have the equation 7(3+7x) = 3(4-2x)

so, I tried 7(3+7x)-3(4-2x)=0

...

Hi there datafiend,

Take the logarithm on both sides of the equation $7^{(3 + 7x)} = 3^{(4 - 2x)}$. This will give you a linear equation in $x$, which you can solve by usual methods.
 

FAQ: Solve Logarithmic Equation: 7(3+7x)-3(4-2x)=0

What is a logarithmic equation?

A logarithmic equation is an equation in which the variable appears in the exponent. It can be solved by using logarithms, which are mathematical operations that involve finding the power to which a base number must be raised to obtain a given number.

How do I solve a logarithmic equation?

To solve a logarithmic equation, you can use the properties of logarithms to rewrite the equation in a simpler form. Then, you can isolate the variable by using basic algebraic techniques such as combining like terms, distributing, and factoring. Once the variable is isolated, you can solve for it by taking the logarithm of both sides and using the inverse property of logarithms.

What are the properties of logarithms?

The properties of logarithms include the product rule, quotient rule, power rule, and logarithmic identities. These properties allow you to manipulate logarithmic expressions and equations in order to solve them.

How do I know when a logarithmic equation has no solutions?

If you end up with a negative number inside the logarithm when solving a logarithmic equation, it means that there are no solutions. This is because logarithms only work with positive numbers. Additionally, if you get an answer that makes the base of the logarithm equal to 0, that equation also has no solutions.

Can I check my solution to a logarithmic equation?

Yes, you can check your solution by plugging it back into the original equation and seeing if it results in a true statement. If it does, then your solution is correct. If it doesn't, then you may have made a mistake in your calculations.

Similar threads

Replies
8
Views
2K
Replies
7
Views
1K
Replies
1
Views
1K
Replies
7
Views
1K
Replies
2
Views
2K
Replies
7
Views
1K
Replies
1
Views
838
Replies
1
Views
905
Replies
10
Views
2K
Back
Top