Questions: Convert the exponential equations into logarithmic form logb C=D : (a) 4^3=64 is equivalent to log4 3= (b) 36=6^2 is equivalent to log6 2= (c) 10^5=100000 is equivalent to log 5= (d) 0.001=10^-3 is equivalent to log =

Convert the exponential equations into logarithmic form logb C=D :
(a) 4^3=64 is equivalent to log4 3=
(b) 36=6^2 is equivalent to log6 2=
(c) 10^5=100000 is equivalent to log 5=
(d) 0.001=10^-3 is equivalent to log =

Transcript text: Convert the exponential equations into logarithmic form $\log _{b} C=D$ : (a) $4^{3}=64$ is equivalent to $\log _{4} 3=$ $\square$ (b) $36=6^{2}$ is equivalent to $\log _{6} 2=$ $\square$ (c) $10^{5}=100000$ is equivalent to $\log 5=$ $\square$ (d) $0.001=10^{-3}$ is equivalent to $\log$ $\square$ $=$ $\square$

Solution

Solution Steps

To convert exponential equations into logarithmic form, we use the relationship between exponents and logarithms. Specifically, if $ b^D = C $, then $ \log_b C = D $.

For each given exponential equation: (a) $ 4^3 = 64 $ can be converted to $ \log_4 64 = 3 $. (b) $ 36 = 6^2 $ can be converted to $ \log_6 36 = 2 $. (c) $ 10^5 = 100000 $ can be converted to $ \log_{10} 100000 = 5 $.

Step 1: Convert $ 4^3 = 64 $ to Logarithmic Form

The equation $ 4^3 = 64 $ can be expressed in logarithmic form as: \[ \log_{4}(64) = 3 \]

Step 2: Convert $ 6^2 = 36 $ to Logarithmic Form

The equation $ 36 = 6^2 $ can be expressed in logarithmic form as: \[ \log_{6}(36) = 2 \]

Step 3: Convert $ 10^5 = 100000 $ to Logarithmic Form

The equation $ 10^5 = 100000 $ can be expressed in logarithmic form as: \[ \log_{10}(100000) = 5 \]