Question

4) Resolver a equação exponencial: 52x – 7 = 125






5) Sendo logb a = 5 e logb c = 3 , encontrar o valor de logb a^2/c =

Answer 1

Explicação passo-a-passo:

4) $5^{2x-7}=125$

$5^{2x-7}=5^3$

$2x-7=3$

$2x=3+7$

$2x=10$

$x=\dfrac{10}{2}$

$\boxed{x=5}$

b) Veja que:

$\text{log}_{b}~\dfrac{a^2}{c}=\text{log}_{b}~a^2-\text{log}_{b}~c$ e $\text{log}_{b}~a^2=2\cdot\text{log}_{b}~a$

Como $\text{log}_{b}~a=5$ e $\text{log}_{b}~c=3$, segue que:

$\text{log}_{b}~\dfrac{a^2}{c}=2\cdot5-3=10-3=7$