Logarithmic Equations (Math Problem Sample)
A logarithmic equation is an equation in which an unknown variable appears as an exponent of a logarithm. Logarithmic equations can be solved using algebraic methods, specifically the properties of logarithms.
The most common type of logarithmic equation is the exponential equation, which is of the form b^x = y. To solve this equation, one would use logarithms to isolate the exponent x. Taking the logarithm of both sides of the equation gives logb(y) = x. This allows one to solve for x using the properties of logarithms.
Logarithmic equations can also involve more complicated expressions, such as logarithmic functions or expressions that contain multiple logarithms. In these cases, the goal is still to isolate the variable by manipulating the logarithmic expressions using the properties of logarithms.
Some common properties of logarithms that can be used to solve logarithmic equations include the product rule, quotient rule, and power rule. These properties allow logarithmic expressions to be simplified and manipulated in a way that makes it possible to solve for the variable.
It is important to note that logarithmic equations may have more than one solution, or no real solutions at all. In cases where there are multiple solutions, it is important to check each solution to ensure it is valid in the original equation.
18 March 2023
By Using the log property of addition, we can write the left side of the equation:
log(x-1) + log(x+1) = log((x-1)(x+1))
So the above equation becomes:
log((x-1)(x+1)) = log21
Using another logarithmic property that if log(a) = log(b) if and only if a = b, so from above equation we can write
(x-1)(x+1) = 21
Expanding the left side of the equation gives:
- Traveling Salesman Problem: Choosing the Shortest Route With Millage ChartDescription: These are the location I decided to pick in US * Vail, CO 81657, 241 S. Frontage Rd., Ste. 8150 It's home to one of the world's largest and most prestigious ski areas. The resort's breathtaking scenery, light powder snow, and overall excellence have earned it a reputation as a top destination. As a whole,...1 page/≈275 words| 2 Sources | APA | Mathematics & Economics | Math Problem |
- Calculations and Operations in Interpreting Social and Economic TrendsDescription: Venture capitalists understand in economics that aggregate revenue is the total receipts a seller acquires from selling products to buyers. It can be represented as P * Q, which is the cost of goods multiplied by the amount/quantity of the products or goods sold. Sellers create plans to capitalize on the...4 pages/≈1100 words| 3 Sources | APA | Mathematics & Economics | Math Problem |
- Advanced mathematicsDescription: Advanced mathematics Mathematics & Economics Math Problem...1 page/≈275 words| No Sources | APA | Mathematics & Economics | Math Problem |