Coco12 said:Homework Statement
6^log x=1/36
2. Homework Equations
Y=logcx
The Attempt at a Solution
How do u solve this? I know the 1/36 is the exponent. Usually the logs that u normally do is not in an exponent like this. The answer is 0.01. How did they get that?
Coco12 said:I thought the ans was -2 since 6^-2 = 1/36
But the ans is 0.01. So that means it is not...
Coco12 said:Is the base 10?
A logarithm is a mathematical function that determines the power to which a base number must be raised to equal a given number. It is the inverse of exponentiation.
To solve a logarithmic equation, you must use the properties of logarithms to rewrite the equation into a simpler form. Then, you can solve for the variable by isolating it on one side of the equation and using the inverse operation of logarithms, which is exponentiation.
The three main properties of logarithms are the product rule, quotient rule, and power rule. The product rule states that the log of the product of two numbers is equal to the sum of the logs of the individual numbers. The quotient rule states that the log of the quotient of two numbers is equal to the difference of the logs of the individual numbers. The power rule states that the log of a number raised to a power is equal to the product of the power and the log of the number.
The natural logarithm, denoted as ln, is a logarithm with a base of e, where e is the mathematical constant approximately equal to 2.71828. It is commonly used in calculus and other areas of mathematics.
Logarithms are used in many real-life applications, such as calculating earthquake intensity, measuring sound levels, and analyzing financial data. They are also commonly used in science and engineering to express large or small quantities in a more manageable form.