Identify base, exponent, and result: Identify the base (b), the exponent (y), and the result (x) in the logarithmic equation log_(4)64. In a logarithmic equation of the form log_(b)x = y, b is the base, x is the result, and y is the exponent. Here, b = 4 and x = 64. We need to find y such that 4^y = 64.Find the value of y: Recall that 64 is a power of 4. Specifically, 64 is 4 raised to the power of 3, because 4 * 4 * 4 = 64. Therefore, y = 3 because 4^3 = 64.Write the exponential form: Write the exponential form of the logarithmic equation log_(4)64. Since we have determined that 4^3 = 64, the exponential form of the equation is 4^3 = 64.

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Algebra 2

Convert between exponential and logarithmic form: all bases

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\log _{4} 64=

Identify base, exponent, and result: Identify the base ( $b$ ), the exponent ( $y$ ), and the result ( $x$ ) in the logarithmic equation $\log_{4}64$ . $\newline$ In a logarithmic equation of the form $\log_{b}x = y$ , $b$ is the base, $x$ is the result, and $y$ is the exponent. $\newline$ Here, $b = 4$ and $x = 64$ . We need to find $y$ such that $y$ $1$ .
Find the value of $y$ : Recall that $64$ is a power of $4$ . Specifically, $64$ is $4$ raised to the power of $3$ , because $4$ \times $4$ \times $4$ = $64$ . $\newline$ Therefore, $y =$ $3$ because $4$ ^ $3$ = $64$ .
Write the exponential form: Write the exponential form of the logarithmic equation $\log_{4}64$ . $\newline$ Since we have determined that $4^3 = 64$ , the exponential form of the equation is $4^3 = 64$ .