Question

2- resolva a equaçao: log (y+3):2 ?
3- considere log3:0,5 e log5:0,7 determine o valor de log10 45?
4- determine o valor da expressao log7 14 sabendo que log 2 : 0,3 e log 7 : 0,8?
5- determine o logaritmo de 343 na base 7?

Answer 1

2)
$log(y+3)=2\\ \\ y+3=10^2\\ \\ y+3=100\\ \\ y=100-3\\ \\ \boxed{y=97}$

3)
$log45=log9.5=log3^2.5=log3^2+log5=2log3+log5=\\ \\ 2*0,5+0,7=1,7$

4)
$log_714=\frac{log14}{log7}=\frac{log2.7}{log7}=\frac{log2+log7}{log7}=\frac{0,3+0,8}{0,8}=1,375$

5)
$log_7343=x\\ \\ 7^x=343\\ \\ 7^x=7^3\\ \\ x=3$