Question

score on last try: 2.86 of 4 pts. see details for more. at least one scored part is incorrect. jump to first changable incorrect part. > next question get a similar question you can retry this question below practice changing between exponential form and logarithmic form using the table below: note: \\(\log_b(a)\\) can be written using an underscore like this: log_b(a). \\(b^c = a\\) \\(\log_b(a) = c\\) \\(5^2 = 25\\) \\(\log_5(25) = 2\\) \\(8^4 = 4096\\) \\(\log_8(4096) = 4\\) \\(3^c = 81\\) \\(\log_4(y) = 6\\) \\(367 = 4^x\\) \\(\log_4(367) = x\\) \\(w = k^{12.5}\\) \\(\log_k(w) = 12.5\\) \\(bumfuzzle = gardyloo^{bigbanana}\\) \\(\log_{gardyloo}(bumfuzzle) = bigbanana\\) question help: video submit question

Explanation:

Step1: Convert \( 3^c = 81 \) to logarithmic form

Recall the relationship \( b^c = a \iff \log_b(a) = c \). Here, \( b = 3 \), \( a = 81 \), and the exponent is \( c \). So the logarithmic form is \( \log_3(81) = c \). We know that \( 3^4 = 81 \), so \( c = 4 \), but following the form, it's \( \log_3(81) = c \).

Step2: Convert \( \log_4(y) = 6 \) to exponential form

Using the same relationship \( \log_b(a) = c \iff b^c = a \). Here, \( b = 4 \), \( c = 6 \), and \( a = y \). So the exponential form is \( 4^6 = y \).

Answer:

For \( 3^c = 81 \), the logarithmic form is \( \log_3(81) = c \); for \( \log_4(y) = 6 \), the exponential form is \( 4^6 = y \).