Solve for x: 4^(x-5) = 7^(2x-1) | Equation Help

  • MHB
  • Thread starter Nikolas7
  • Start date
In summary, an equation is a mathematical statement that shows the relationship between quantities using numbers, variables, and mathematical operations. To solve an equation, the variable must be isolated on one side of the equal sign by using the same operation on both sides. There are various types of equations, each with their own specific methods for solving. The order of operations is important when solving equations, which includes parentheses, exponents, multiplication and division (left to right), and addition and subtraction (left to right). Common mistakes to avoid when solving equations include not performing the same operation on both sides, making calculation errors, and not checking the solution back into the original equation for accuracy.
  • #1
Nikolas7
22
0
Help me with the following equation:
${4}^{x-5}$=${7}^{2x-1}$
 
Mathematics news on Phys.org
  • #2
Nikolas7 said:
Help me with the following equation:
${4}^{x-5}$=${7}^{2x-1}$

you can take log on both sides and get $(x-5)\log\, 4 = (2x-1) log\, 7$ and because it is linear equation you can proceed to finish it
 
  • #3
Please, show details how you got (x−5)log4=(2x−1)log7
 
  • #4
Nikolas7 said:
Please, show details how you got (x−5)log4=(2x−1)log7

this is as per definition $\log\,a ^ x = x \log\, a $
 
  • #5
Yes, I figured out, thanks
 

FAQ: Solve for x: 4^(x-5) = 7^(2x-1) | Equation Help

What is an equation?

An equation is a mathematical statement that shows the relationship between two or more quantities. It usually consists of numbers, variables, and mathematical operations.

How do I solve an equation?

To solve an equation, you must isolate the variable on one side of the equal sign by performing the same operation on both sides of the equation. This will result in the value of the variable being determined.

What are the different types of equations?

There are many different types of equations, such as linear equations, quadratic equations, exponential equations, and trigonometric equations. Each type has its own specific methods for solving.

Is there a specific order to solving equations?

Yes, there is a specific order to solving equations, known as the order of operations. This order is parentheses, exponents, multiplication and division (left to right), and addition and subtraction (left to right).

What are some common mistakes to avoid when solving equations?

Some common mistakes to avoid when solving equations include forgetting to perform the same operation on both sides of the equation, making calculation errors, and not checking the solution back into the original equation to ensure it is correct.

Similar threads

Replies
7
Views
1K
Replies
1
Views
839
Replies
6
Views
1K
Replies
4
Views
1K
Replies
8
Views
985
Replies
2
Views
1K
Replies
5
Views
2K
Replies
14
Views
2K
Replies
3
Views
1K
Replies
4
Views
1K
Back
Top