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

1. 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.

2. 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.

3. 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.

4. 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).

5. 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

MHB Solve Equation: $x^4+2x^3-x^2-6x-3=0$
Replies
7
Views
1K
MHB -s6.6 solve exponential eq 3^x-14\cdot 3^{-x}=5
Replies
1
Views
783
MHB 5.6.28 find domain of x in ABS
Replies
6
Views
977
MHB Solving the Equation: x+[2x]+[3x]=7
Replies
4
Views
1K
MHB How can you solve $5^{x^2+8}=125^{2x}$ for x?
Replies
8
Views
922
MHB Solve Floor Equation 7: x^2=2x-1
Replies
2
Views
1K
MHB Make x the subject of 2x/5-3b/4=x+5
Replies
5
Views
2K
MHB Solving the Floor Function Equation: $[x]=2x+1$
Replies
14
Views
2K
MHB Solve the Floor Value of x in $x^2+1=2x$
Replies
3
Views
986
MHB Equation 2: Prove that ##x^2+2x\sqrt x+3x+2\sqrt x+1=0##
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top