Question

Como resolve essa função de logaritimo? 3.000 = (1,25)^t

Answer 1

A sua pergunta esta incompleta, entretanto vou considera os dados como:

⇒ ㏒ 3 = 0,48
⇒ ㏒ 5 = 0,7
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$3000=\left(1,25\right)^t\\3\cdot 10^3=\left(1,25\right)^t\\log\:\left(3\cdot \:10^3\right)=log\:\left(1,25\right)^t\\log\:\left(3\right)+log\:\left(\:10^3\right)=log\:\left(1,25\right)^t\\log\:\left(3\right)+3\cdot log\:\left(10\right)=t\cdot log\:\left(1,25\right)\\log\:\left(3\right)+\left(3\cdot 1\right)=t\cdot log\:\left(1,25\right)\\log\:\left(3\right)+3=t\cdot log\:\left(1,25\right)\\log\left(3\right)+3=t\cdot log\:\left(\frac{125}{100}\right)$
$log\left(3\right)+3=t\cdot \left\{log\:\left(125\right)-log\:\left(100\right)\right\}\\log\left(3\right)+3=t\cdot \left\{log\:\left(5^3\right)-2\right\}\\log\left(3\right)+3=t\cdot \left\{3\cdot log\:\left(5\right)-2\right\}\\0,48+3=t\cdot \:\left\{\left(3\cdot \:0,7\right)-2\right\}\\3,48=t\cdot \:\left(2,1-2\right)\\3,48=0,1t\\\boxed{\bold{t\approx \:34,8}}$