Question

Write the exponential equation for the logarithmic equation. log₆216 = 3

a) 6³ = 216
b) 6² = 216
c) 6⁴ = 216
d) 6⁵ = 216

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf log_6\:216 = 3$}`

`\Large \boxed{\boxed{\text{$ \sf 6^3 = 216$}}}`

Answer 2

The correct exponential equation for the logarithmic equation log₆ 216 = 3 is 63 = 216, which is option (a). The property used for this conversion states that if logb(a) = c, then bc= a.

Step-by-step explanation:

To convert the logarithmic equation log₆ 216 = 3 to an exponential equation, we can use the property that states, if logb(a) = c, then bc = a. This means that the base (6 in this case) raised to the logarithm's result (3 here) equals the number that was inside the log (which is 216). Therefore, the equivalent exponential equation is 63 = 216.

Let's review the options given:

• a) 63 = 216 is correct based on our conversion.
• b) 62 = 216 is incorrect since 6 squared is 36, not 216.
• c) 64 = 216 is incorrect as 6 to the fourth power is 1296.
• d) 65 = 216 is also incorrect since 6 to the fifth power is a much larger number.

Therefore, the correct exponential equation for the logarithmic equation log₆ 216 = 3 is option a) 6^3= 216