Solve for z. 6^z = 36 z = ____

Recognize Equation Format: Recognize the equation format. We have 6^z = 36. We need to find the value of z that makes this equation true.Express as Power of 6: Express 36 as a power of 6. Since 36 is 6 squared (6^2), we can rewrite the equation as 6^z = 6^2.Equate Exponents: Equate the exponents. If 6^z = 6^2, then z must equal 2 because the bases are the same and thus the exponents must be equal.

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Solve for $z$ . $\newline$ $6^z = 36$ $\newline$ $z = \_\_\_$

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Math Problems

Grade 8

Solve equations with variable exponents

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Q. Solve for

z

\newline

6^z = 36

\newline

z = \_\_\_

Recognize Equation Format: Recognize the equation format. $\newline$ We have $6^z = 36$ . We need to find the value of $z$ that makes this equation true.
Express as Power of $6$ : Express $36$ as a power of $6$ . $\newline$ Since $36$ is $6$ squared ( $6^2$ ), we can rewrite the equation as $6^z = 6^2$ .
Equate Exponents: Equate the exponents. $\newline$ If $6^z = 6^2$ , then $z$ must equal $2$ because the bases are the same and thus the exponents must be equal.