logarithms
x
=
Step by step worksheet, laws of logarithm

Solves equation in this form $2^x=5$

# Logarithmsbasecalculator

Logarithms base calculator solves equations involving power with step by step worksheet.
Solve logarithm in this form

Enter 2^x = 5

### step 2: Getting it right

To rasie any exponent, use the caret symbol " ^ "

### result

Hit the check mark to solve for logarithms.

### What is Logarithms Base?

Logarithm base is the number that the logarithm is taken with respect to. It determines the behavior and properties of the logarithmic function.

### Logarithms Base Rules

#### 1. Logarithm of a product

This rule states that the logarithm of a product is equal to the sum of the logarithms of the individual factors.

#### 2. Logarithm of a quotient

This rule states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator.

#### 3. Logarithm of a power

This rule states that the logarithm of a power is equal to the product of the exponent and the logarithm of the base.

#### Example 1 Without Changing the Base

To solve the equation 2^x = 5, take the logarithm (base 2) of both sides to eliminate the exponent.

• log_2(2^x) = log_2(5)

• Using the logarithmic property that states if log_b(x^y) = y * log_b(x), you can simplify the equation:

• x * log_2(2) = log_2(5)

• Since log_2(2) = 1, we have:

• x = log_2(5)

• Using a calculator, we can evaluate log_2(5) to be approximately 2.3219.

• Hence, the solution to the equation

• 2^x = 5 is

• x ≈ 2.3219.

#### Example 2, Using Base 10

To solve the equation 2^x = 8 using base 10, we can take the logarithm (base 10) of both sides to eliminate the exponent.

• log_10(2^x) = log_10(8)

• Using the logarithmic property that states if log_b(x^y) = y * log_b(x), we can simplify the equation:

• x * log_10(2) = log_10(8)

• Since log_10(2) is a constant, we can evaluate it to be approximately 0.3010.

• x * 0.3010 = log_10(8)

• Using a calculator, we can evaluate log_10(8) to be approximately 0.9031.

• x * 0.3010 = 0.9031

• Simplifying further, we can solve for x:

• x ≈ 0.9031 / 0.3010
x ≈ 2.999

• Therefore, the solution to the equation 2^x = 8 using base 10 is x ≈ 2.999.

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