logarithms

x

=

Step by step worksheet, laws of logarithm

Solves equation in this form \[ 2^x=5\]

Logarithms base calculator solves equations involving power with step by step worksheet.

Solve **logarithm ** in this form

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

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

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

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

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

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