# What is logarithmic equations and inequalities?

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A logarithmic equation or inequality can be solved for all x values that satisfy the equation or inequality. (Lesson 21). A logarithmic function expresses a relationship between two variables (such as x and y), and can be represented by a table of values or a graph (Lesson 22).

Then, what is logarithmic inequality?

Logarithmic inequalities are inequalities in which one (or both) sides involve a logarithm. Like exponential inequalities, they are useful in analyzing situations involving repeated multiplication, such as in the cases of interest and exponential decay.

Likewise, what is logarithmic equation? A logarithmic equation is an equation that involves the logarithm of an expression containing a variable. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.

Accordingly, what is logarithmic function example?

A logarithm is an exponent. The exponential function is written as: f(x) = bx. The logarithmic function is written as: f(x) = log base b of x. The common log uses the base 10. The natural log uses the base e, which is an irrational number, e = 2.71828.

What is the property of log?

Recall that we use the product rule of exponents to combine the product of exponents by adding: xaxb=xa+b x a x b = x a + b . We have a similar property for logarithms, called the product rule for logarithms, which says that the logarithm of a product is equal to a sum of logarithms.

### What are logarithmic functions?

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. y = logax only under the following conditions: x = ay, a > 0, and a≠1.

### How do you solve an inequality?

To solve an inequality use the following steps:
1. Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.
2. Step 2 Simplify by combining like terms on each side of the inequality.
3. Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

### What is a logarithm in simple terms?

A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2.

### What are the laws of logarithms?

The laws apply to logarithms of any base but the same base must be used throughout a calculation. This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB. The same base, in this case 10, is used throughout the calculation.

### What is exponential inequality?

Exponential inequalities are inequalities in which one (or both) sides involve a variable exponent. They are useful in situations involving repeated multiplication, especially when being compared to a constant value, such as in the case of interest.

### Does log change inequality?

No, you don't. Taking the log doesn't change which way an inequality points (except in a special case we'll get to at the end of this answer). So subtracting also sometimes turns positive numbers into negative numbers, but it doesn't involve flipping the inequality sign.

### Can you take the log of both sides of an inequality?

You can take the logarithm on both sides of the inequality, if you know the numbers are positive.

### What is LN equal to?

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.

### What is the inverse of log?

Some functions in math have a known inverse function. The log function is one of these functions. We know that the inverse of a log function is an exponential. So, we know that the inverse of f(x) = log subb(x) is f^-1(y) = b^y.

### What is a logarithmic relationship?

log·a·rithm
The power to which a base, such as 10, must be raised to produce a given number. For example, 103 = 1,000; therefore, log10 1,000 = 3. The kinds most often used are the common logarithm (base 10), the natural logarithm (base e), and the binary logarithm (base 2).

### Why do we use logarithmic functions?

There are two main reasons to use logarithmic scales in charts and graphs. The first is to respond to skewness towards large values; i.e., cases in which one or a few points are much larger than the bulk of the data. The second is to show percent change or multiplicative factors.

### What is the purpose of a logarithmic function?

Working Definition of Logarithm
The purpose of the inverse of a function is to tell you what x value was used when you already know the y value. So, the purpose of the logarithm is to tell you the exponent. Thus, our simple definition of a logarithm is that it is an exponent.

### What's the difference between logarithmic and exponential?

This means that the function is an increasing function. The inverse of an exponential function is a logarithmic function and the inverse of a logarithmic function is an exponential function. Notice also on the graph that as x gets larger and larger, the function value of f(x) is increasing more and more dramatically.