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Question Number 191155 by mathlove last updated on 19/Apr/23

Answered by mahdipoor last updated on 19/Apr/23

$$log\left(xy\right)=log\left(x\right)+log\left(y\right)\Rightarrow x=a,y=1+\frac{b}{a}\Rightarrow$$$$log(a+b)=log\left(a\right)+log(1+b/a)$$$$........$$$$b={10}^B,a={10}^A,c={10}^C$$$${\left(\frac{b}{c}\right)}^{loga}={\left({10}^{B-C}\right)}^A={10}^{BA-CA}...$$$$\Rightarrow {10}^{BA-CA}\times {10}^{CB-AB}\times {10}^{AC-BC}={10}^0=1$$

Commented by mathlove last updated on 19/Apr/23

$$tnks$$

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