Write the exponential equation 72 9 2 / 3 = 81 729 ^ { 2 / 3 } = 81 72 9 2/3 = 81 in logarithmic form.A) log ⁡ 729 81 = 2 3 \log _ { 729 } 81 = \frac { 2 } { 3 } lo g 729 81 = 3 2 B) log ⁡ 9 729 = 9 \log _ { 9 } 729 = 9 lo g 9 729 = 9 C) log ⁡ 9 81 = 2 \log _ { 9 } 81 = 2 lo g 9 81 = 2 D) log ⁡ 729 81 = 3 2 \log _ { 729 } 81 = \frac { 3 } { 2 } lo g 729 81 = 2 3 E) log ⁡ 729 81 = 3 \log _ { 729 } 81 = 3 lo g 729 81 = 3

Question

Write the exponential equation   72 9 2 / 3 = 81 729 ^ { 2 / 3 } = 81 72 9 2/3 = 81   in logarithmic form.A)    log ⁡ 729 81 = 2 3 \log _ { 729 } 81 = \frac { 2 } { 3 } lo g 729 ​ 81 = 3 2 ​ B)    log ⁡ 9 729 = 9 \log _ { 9 } 729 = 9 lo g 9 ​ 729 = 9 C)    log ⁡ 9 81 = 2 \log _ { 9 } 81 = 2 lo g 9 ​ 81 = 2 D)    log ⁡ 729 81 = 3 2 \log _ { 729 } 81 = \frac { 3 } { 2 } lo g 729 ​ 81 = 2 3 ​ E)    log ⁡ 729 81 = 3 \log _ { 729 } 81 = 3 lo g 729 ​ 81 = 3

Makaila Warga · Accepted Answer

Final Answer : A, Explanation :   The exponential equation   72 9 2 / 3 = 81 729^{2/3} = 81 72 9 2/3 = 81   can be rewritten in logarithmic form as   log ⁡ 729 81 = 2 3 \log_{729} 81 = \frac{2}{3} lo g 729 ​ 81 = 3 2 ​  , which matches choice A. This is because the logarithmic form   log ⁡ b a = c \log_b a = c lo g b ​ a = c   corresponds to the exponential form   b c = a b^c = a b c = a  .

Write the exponential equation $729 ^ { 2 / 3 } = 81$ in logarithmic form.

A) $log⁡72981=23\log _ { 729 } 81 = \frac { 2 } { 3 }$
B) $log _ { 9 } 729 = 9$
C) $log _ { 9 } 81 = 2$
D) $log⁡72981=32\log _ { 729 } 81 = \frac { 3 } { 2 }$
E) $log _ { 729 } 81 = 3$

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