## How do you compare log values with different bases?

To solve this type of problem:

- Step 1: Change the Base to 10. Using the change of base formula, you have.
- Step 2: Solve for the Numerator and Denominator. Since your calculator is equipped to solve base-10 logarithms explicitly, you can quickly find that log 50 = 1.699 and log 2 = 0.3010.
- Step 3: Divide to Get the Solution.

## Can you combine logs with different bases?

No. There is a change of base formula for converting between different bases. To find the log base a, where a is presumably some number other than 10 or e, otherwise you would just use the calculator, Take the log of the argument divided by the log of the base.

**What are the three properties of logarithms?**

Logarithm Base Properties

- Product rule: am. an=a. m+n
- Quotient rule: am/an = a. m-n
- Power of a Power: (am)n = a. mn

**How do you explain the properties of logarithms?**

The logarithmic number is associated with exponent and power, such that if xn = m, then it is equal to logx m=n….Comparison of Exponent law and Logarithm law.

Properties/Rules | Exponents | Logarithms |
---|---|---|

Quotient Rule | xp/xq = xp-q | loga(m/n) = logam – logan |

Power Rule | (xp)q = xpq | logamn = n logam |

### How can exponential equations with unequal bases be solved?

In general we can solve exponential equations whose terms do not have like bases in the following way:

- Apply the logarithm to both sides of the equation. If one of the terms in the equation has base 10 , use the common logarithm.
- Use the rules of logarithms to solve for the unknown.

### What is the change of base formula for logarithms?

Sometimes, however, you may need to solve logarithms with different bases. This is where the change of base formula comes in handy: log bx = log ax/log ab. This formula allows you to take advantage of the essential properties of logarithms by recasting any problem in a form that is more easily solved.

**What is a logarithmic expression in math?**

A logarithmic expression in mathematics takes the form. y = log bx. where y is an exponent, b is called the base and x is the number that results from raising the b to the power of y.

**What is the relationship between logarithmic and exponential forms?**

The relationship between logarithmic and exponential forms allows us to deduce the properties satisfied by the logarithmic forms, known as the laws of logarithms, that follow from the laws of exponents. Let’s recall the laws of logarithms.