# How can you use the properties of logarithms to condense logarithmic expressions?

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Condense logarithmic expressions
1. Apply the power property first. Identify terms that are products of factors and a logarithm, and rewrite each as the logarithm of a power.
2. Next apply the product property. Rewrite sums of logarithms as the logarithm of a product.
3. Apply the quotient property last.

Hereof, what does it mean to condense a logarithmic expression?

When they tell you to "simplify" a log expression, this usually means they will have given you lots of log terms, each containing a simple argument, and they want you to combine everything into one log with a complicated argument. "Simplifying" in this context usually means the opposite of "expanding".

Similarly, 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.

One may also ask, how do you do properties of logarithms?

The logarithm of a product property says log2 8a = log2 8 + log2 a, and log2 8 = 3. You can use the similarity between the properties of exponents and logarithms to find the property for the logarithm of a quotient. With exponents, to multiply two numbers with the same base, you add the exponents.

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 are the log properties?

Properties of Logarithms
logb1=0 log b 1 = 0 . This follows from the fact that b0=1 b 0 = 1 . logbb=1 log b b = 1 . This follows from the fact that b1=b b 1 = b . logbbx=x log b b x = x .

### What is the function of log?

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

### What are the four properties of logarithms?

Logs have four basic properties:
• Product Rule: The log of a product is equal to the sum of the log of the first base and the log of the second base ( ).
• Quotient Rule: The log of a quotient is equal to the difference of the logs of the numerator and denominator ( ).

Logarithms are a convenient way to express large numbers. (The base-10 logarithm of a number is roughly the number of digits in that number, for example.) Slide rules work because adding and subtracting logarithms is equivalent to multiplication and division. (This benefit is slightly less important today.)

### How do you express powers as a factor?

write the expression as a single logarithm express powers as factors must show work
1. combine + terms with multiplication.
2. cancel common factors.
3. combine - terms with division.
4. cancel common factors.
5. write as negative exponent.
6. use power rule.

### Can you distribute a log?

Can you distribute log on log(x+y)? In general, no. The logarithm of a sum is as simplified as it gets, unless the sum itself can in some way be simplified. (For instance log(5 + 3) = log(8)).

### 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 exactly is a log?

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 properties of logarithms and examples?

Properties of Logarithms
1. loga (uv) = loga u + loga v 1. ln (uv) = ln u + ln v
2. loga (u / v) = loga u - loga v 2. ln (u / v) = ln u - ln v
3. loga un = n loga u 3. ln un = n ln u

### What are the 3 properties of logarithms?

Throughout your study of algebra, you have come across many properties—such as the commutative, associative, and distributive properties. These properties help you take a complicated expression or equation and simplify it. The same is true with logarithms.

### Why can't logarithms have negative bases?

So 0, 1, and every negative number presents a potential problem as the base of a power function. And if those numbers can't reliably be the base of a power function, then they also can't reliably be the base of a logarithm. For that reason, we only allow positive numbers other than 1 as the base of the logarithm.

### What does Ln mean?

natural logarithm

### What is the one to one property of logarithms?

The one-to-one property of logarithmic functions tells us that, for any real numbers x > 0, S > 0, T > 0 and any positive real number b, where b≠1 b ≠ 1 , logbS=logbT if and only if S=T l o g b S = l o g b T if and only if S = T .

### What is the log of 0?

log 0 is undefined. The result is not a real number, because you can never get zero by raising anything to the power of anything else. You can never reach zero, you can only approach it using an infinitely large and negative power. The real logarithmic function logb(x) is defined only for x>0.