Identify base and number: Identify the base and the number for which we are finding the logarithm. The base is 3 and the number is 9.Recall logarithm definition: Recall the definition of a logarithm. The logarithm log_base(b)(a) is the exponent to which the base b must be raised to obtain the number a.Determine exponent: Determine the exponent that makes the base equal to the number. We need to find the exponent x such that 3^x = 9.Solve equation: Solve the equation 3^x = 9. Since 9 is 3 squared (3^2), we can see that x = 2.Conclude logarithm value: Conclude the value of the logarithm. Therefore, log_(3)9 = 2.

Grade 7

Add, subtract, multiply, and divide integers

Full solution

\log _{3} 9=

Identify base and number: Identify the base and the number for which we are finding the logarithm. $\newline$ The base is $3$ and the number is $9$ .
Recall logarithm definition: Recall the definition of a logarithm. $\newline$ The logarithm $\log_{\text{base}}(b)(a)$ is the exponent to which the base $b$ must be raised to obtain the number $a$ .
Determine exponent: Determine the exponent that makes the base equal to the number. $\newline$ We need to find the exponent $x$ such that $3^x = 9$ .
Solve equation: Solve the equation $3^x = 9$ . $\newline$ Since $9$ is $3$ squared ( $3^2$ ), we can see that $x = 2$ .
Conclude logarithm value: Conclude the value of the logarithm. $\newline$ Therefore, $\log_{3}9 = 2$ .