Q&A for How to Understand Logarithms

Here are some few practice problems : 1. log(3 + 2 log(1+x) ) =0 , Find x 2. If (2.5)^x = 0.025)^y, find x and y.

You must expand the expression to 6=log(x)-log(5). This is an example of the quotient property of a logarithm log(a/b)=log(a)-log(b). You then do log(5), which is approximately 0.699, so 6=log(x)-0.699. Add 0.699 to both sides to get 6.699=log(x). Then rewrite it in exponential form as 10^6.699=x and do the rest.

The ln(y) function is similar to a log function. A log function uses a base of ten (log base ten of x is often written log(x)), unless otherwise specified. A function ln(x) is just a logarithm with a base of e, a number that is similar to pi in the fact that it is a mathematical constant. The letter e represents the number 2.71828. So, ln(y) is equivalent to log of y with a base of e, or log base e of y.

X is a variable. In a logarithm, the value to be found is denoted by X. (It can be either the base or argument.)

You can find the solution of a negative log, however the number that you find will not be rational so for all intents and purposes you cannot.

Logarithms provide a tool to solve problems. Another way to think of this, logarithms rewrite problems to indicate exponential numbers without using any powers in the actual equation. Logarithms provides greater access to all the numbers in the equation. This is the basic purpose of a log.

Simplify the left side to a single log (x^2-1). Then take the antilog of both sides (x^2-1=3). Solve resultant polynomial equation (x=2 or x= -2). Check solutions against original equation for domain issues. For example, if x=-2, log (x-1) is undefined, so it is not the correct solution.

That means 3 times the log of 4. The log (base 10) of 4 is approximately 0.6. 3 times 0.6 is 1.8. 1.8 is the antilog of 64. This is just another way of saying 4³ = 64.

Notice they have the same base, You can then make this into log base 2 of (3x + 1 / 2x - 7) = 3. Make 2 the base on both sides. 3x + 1 / 2x - 7 = 8. Multiply both sides by the denominator. 3x + 1 = 8(2x - 7). 3x + 1 = 16x - 56. Add 56 to both sides and subtract 3x on both sides. 57 = 19x. Divide both sides by 19, so that x = 3.

You can't solve this for a value of a number because there are two unknowns in one equation. However, if it was log x + 2log x = 4, you can solve it this way: log x + 2logx = 3log x = 4, therefore dividing by 3 on both sides: log x = 4/3. Raising exponents of 10 on each side: x = 10^(4/3).

Using the two rules of logarithms, we know that log a + log b (a and b are positive numbers) = log(a×b), similarly log a - log b = log(a / b). There is also this relationship: log(a^n) = n×log(a).

It's recommended to use a calculator for that one, as it is very hard and difficult to do it manually. In the numerator, evaluate each log separately, add the two logs together, then work on the denominators logs doing it the same way.