Log15sqrt15 Without Calculator

What is log15√15?

The expression log15√15 represents a logarithm with base 15 of the square root of 15. In mathematical terms, it can be written as:

This expression asks for the exponent to which 15 must be raised to obtain the square root of 15. The result is a value that represents how many times 15 needs to be multiplied by itself to equal √15.

How to calculate log15√15

To calculate log15√15 without a calculator, follow these steps:

1. Understand that √15 is the same as 15 raised to the power of 1/2.
2. Apply the logarithm power rule: log_a(b^c) = c * log_a(b).
3. Calculate log₁₅(15) which equals 1.
4. Multiply the result by 1/2 (the exponent).

Step-by-step guide

Step 1: Understand the components

The expression log15√15 consists of two main parts:

• The base of the logarithm is 15
• The argument is √15 (the square root of 15)

Step 2: Apply logarithm properties

Use the logarithm power rule which states that log_a(b^c) = c * log_a(b).

Step 3: Simplify the expression

Since √15 is 15 raised to the power of 1/2, we can rewrite the expression as:

log₁₅(15^1/2) = (1/2) * log₁₅(15)

Step 4: Calculate the logarithm

Any logarithm of a number with the same base equals 1. Therefore, log₁₅(15) = 1.

Step 5: Final calculation

Multiply the result by 1/2 to get the final answer:

(1/2) * 1 = 0.5

Example calculation

Let's work through a practical example to understand how to calculate log15√15:

Common mistakes

When calculating log15√15, be aware of these common errors:

• Forgetting to apply the logarithm power rule correctly
• Incorrectly calculating log₁₅(15) as something other than 1
• Miscounting the multiplication by 1/2
• Confusing the base and argument of the logarithm

Double-check each step to ensure accuracy in your calculations.