Identify base and argument: Identify the base (b) and the argument (x) of the logarithm. In the expression log₂(128), the base b is 2 and the argument x is 128.Recall logarithm definition: Recall the definition of a logarithm. The logarithmic equation log₂(x) = y is equivalent to the exponential equation 2^y = x.Find exponent for equation: Find the exponent (y) that makes the equation 2^y = 128 true. We know that 2^7 = 128 because 2 * 2 * 2 * 2 * 2 * 2 * 2 = 128.Write equation in exponential form: Write the logarithmic equation in exponential form. Since 2^7 = 128, we can write log₂(128) = 7.

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$\log _{2} 128=$

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Algebra 2

Convert between exponential and logarithmic form: all bases

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\log _{2} 128=

Identify base and argument: Identify the base (b) and the argument (x) of the logarithm. $\newline$ In the expression $\log_2(128)$ , the base $b$ is $2$ and the argument $x$ is $128$ .
Recall logarithm definition: Recall the definition of a logarithm. $\newline$ The logarithmic equation $\log_2(x) = y$ is equivalent to the exponential equation $2^y = x$ .
Find exponent for equation: Find the exponent ( $y$ ) that makes the equation $2^y = 128$ true. $\newline$ We know that $2^7 = 128$ because $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 128$ .
Write equation in exponential form: Write the logarithmic equation in exponential form. $\newline$ Since $2^7 = 128$ , we can write $\log_2(128) = 7$ .