Identify base, argument, and unknown exponent: Identify the base (b), the argument (x), and the unknown exponent (y) in the logarithmic equation log_(3)243 = y. In this case, b = 3 and x = 243. We need to find the value of y such that 3^y = 243.Recall logarithms and exponents relationship: Recall the relationship between logarithms and exponents: log_(b)x = y is equivalent to b^y = x. We can rewrite the logarithmic equation in exponential form: 3^y = 243.Determine the value of y: Determine the value of y by finding the exponent that makes 3^y equal to 243. We know that 3^5 = 243 because 3 * 3 * 3 * 3 * 3 = 243. Therefore, y = 5.Write the final exponential equation: Write the final exponential equation using the value of y found in the previous step. The exponential form of the equation is 3^5 = 243.

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\log _{3} 243=$

View step-by-step help

Home

Math Problems

Algebra 2

Convert between exponential and logarithmic form: all bases

Full solution

\log _{3} 243=

Identify base, argument, and unknown exponent: Identify the base (), the argument (), and the unknown exponent () in the logarithmic equation _{( $3$ )} $243$ = . In this case, = $3$ and = $243$ . We need to find the value of such that $3$ ^ = $243$ .
Recall logarithms and exponents relationship: Recall the relationship between logarithms and exponents: $\log_{b}x = y$ is equivalent to $b^{y} = x$ . $\newline$ We can rewrite the logarithmic equation in exponential form: $3^{y} = 243$ .
Determine the value of $y$ : Determine the value of $y$ by finding the exponent that makes $3^y$ equal to $243$ . $\newline$ We know that $3^5 = 243$ because $3 \times 3 \times 3 \times 3 \times 3 = 243$ . $\newline$ Therefore, $y = 5$ .
Write the final exponential equation: Write the final exponential equation using the value of $y$ found in the previous step. $\newline$ The exponential form of the equation is $3^5 = 243$ .