Questions: Fill in each box below with an integer or a reduced fraction. (a) log8 2 = 1/3 can be written in the form A^B = C where A= , B= , and C= (b) log2(1/8) = -3 can be written in the form D^E = F where D= , E= , and F= Question Help: Video Submit Question

$Fill in each box below with an integer or a reduced fraction. (a) log8 2 = 1/3 can be written in the form A^B = C where A= , B= , and C= (b) log2(1/8) = -3 can be written in the form D^E = F where D= , E= , and F= Question Help: Video Submit Question$

Transcript text: Fill in each box below with an integer or a reduced fraction. (a) $\log _{8} 2=\frac{1}{3}$ can be written in the form $A^{B}=C$ where $A=\square, B=\square$, and $C=$ $\square$ (b) $\log _{2}\left(\frac{1}{8}\right)=-3$ can be written in the form $D^{E}=F$ where $D=$ $\square$ , $E=$ $\square$ , and $F=$ $\square$ Question Help: $\square$ Video Submit Question

Solution

Solution Steps

Solution Approach

(a) To convert the logarithmic equation $\log_{8} 2 = \frac{1}{3}$ into the exponential form $A^B = C$, we need to identify the base $A$, the exponent $B$, and the result $C$. The base $A$ is 8, the exponent $B$ is $\frac{1}{3}$, and the result $C$ is 2.

(b) To convert the logarithmic equation $\log_{2} \left(\frac{1}{8}\right) = -3$ into the exponential form $D^E = F$, we need to identify the base $D$, the exponent $E$, and the result $F$. The base $D$ is 2, the exponent $E$ is -3, and the result $F$ is $\frac{1}{8}$.

Step 1: Convert Logarithmic Equation (a)

We start with the equation $ \log_{8} 2 = \frac{1}{3} $. To express this in exponential form, we rewrite it as: \[ 8^{\frac{1}{3}} = 2 \] Here, we identify $ A = 8 $, $ B = \frac{1}{3} $, and $ C = 2 $.

Step 2: Convert Logarithmic Equation (b)

Next, we consider the equation $ \log_{2} \left(\frac{1}{8}\right) = -3 $. We convert this to exponential form: \[ 2^{-3} = \frac{1}{8} \] In this case, we have $ D = 2 $, $ E = -3 $, and $ F = \frac{1}{8} $.