# How do you find equivalent logarithms?

## How do you find equivalent logarithms?

Every equation that is in exponential form has an equivalent logarithmic form, and vice versa. Both equations have a ‘b,’ the base, an x, and a y. These two equations are equivalent, just like these two equations are equivalent: y = x + 9 and y – 9 = x. Using algebra, you can get from one to the other.

**How do you subtract logarithms?**

To subtract logs, just divide the inputs (numbers inside the log). The rule logb(x/y) = logb(x) – log_b(y) lets you “convert division to log subtraction”. It’s actually just the “log version” of the quotient rule for exponents.

**How do you divide logarithms?**

Division. The rule when you divide two values with the same base is to subtract the exponents. Therefore, the rule for division is to subtract the logarithms. The log of a quotient is the difference of the logs.

### Can the base of a log be negative?

While the value of a logarithm itself can be positive or negative, the base of the log function and the argument of the log function are a different story. The argument of a log function can only take positive arguments. In other words, the only numbers you can plug into a log function are positive numbers.

**What are the rules of logarithms?**

The rules apply for any logarithm logbx, except that you have to replace any occurence of e with the new base b. The natural log was defined by equations (1) and (2)….Basic rules for logarithms.

Rule or special case | Formula |
---|---|

Quotient | ln(x/y)=ln(x)âln(y) |

Log of power | ln(xy)=yln(x) |

Log of e | ln(e)=1 |

Log of one | ln(1)=0 |

**How do you combine subtracting logs?**

Logs of the same base can be added together by multiplying their arguments: log(xy) = log(x) + log(y). They can be subtracted by dividing the arguments: log(x/y) = log(x) – log(y).

#### Why can’t a logarithm have a base of 1?

log 0 is undefined. It’s not a real number, because you can never get zero by raising anything to the power of anything else. log 1 = 0 means that the logarithm of 1 is always zero, no matter what the base of the logarithm is. This is because any number raised to 0 equals 1.

**Why are there no negative logarithms?**

And as you know, unless we’re getting into imaginary numbers, we can’t deal with a negative number underneath a square root. So in summary, because the we only allow the log’s base to be a positive number not equal to 1, that means the argument of the logarithm can only be a positive number.

**How are the rules of the logarithm expressed?**

Logarithm Rules. In less formal terms, the log rules might be expressed as: 1) Multiplication inside the log can be turned into addition outside the log, and vice versa. 2) Division inside the log can be turned into subtraction outside the log, and vice versa.

## Which is the simplifying equation for log2 ( 8 )?

Simplify log2 (8). This log is equal to some number, which I’ll call y. This naming gives me the equation log2 (8) = y. Then the Relationship says: That is, log2 (8), also known as y, is the power that, when put on 2, will turn 2 into 8.

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**How to simplify the relationship of log3 and log4?**

The Relationship says that, since log3 (1) = y, then 3 y = 1. But 1 = 3 0, so 3 y = 3 0, and y = 0. That is: This is always true: logb (1) = 0 for any base b, not just for b = 3. Simplify log4 (â16). The Relationship says that, since log4 (â16) = y, then 4 y = â16. But wait! What power y could possibly turn a positive 4 into a negative 16?