Sagot :
Answer:
1/3
Step-by-step explanation:
[tex]\rm 69.42^a = 277.68^b = 64[/tex]
[tex]\implies \rm a = \frac{\ln64}{\ln69.42}[/tex]
[tex]\implies \rm b = \frac{\ln64}{\ln277.68}[/tex]
[tex]\rm \therefore \frac{1}{b} - \frac{1}{a} = \frac{1}{\frac{\ln64}{\ln277.68} } - \frac{1}{\frac{\ln64}{\ln69.42} }[/tex]
[tex]\implies \rm \frac{1}{b} - \frac{1}{a} = \frac{\ln277.68 - \ln69.42}{\ln64}[/tex]
[tex]\implies \rm \frac{1}{b} - \frac{1}{a} = \frac{\frac{\ln277.68}{\ln69.42} }{\ln64}[/tex]
[tex]\implies \rm \frac{\ln4}{\ln64}[/tex]
[tex]\implies \frac{\ln4}{\ln4^3}[/tex]
[tex]\implies \boxed{\rm \frac{1}{3}}[/tex]
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