Answer:
Step-by-step explanation:
From table 1,
f(x) = bˣ
For x = -1,
f(-1) = 0.5
0.5 = (b)⁻¹
b = [tex]\frac{1}{0.5}[/tex]
b = 2
For x = 1.585,
f(1.585) = 3
3 = [tex]2^{1.585}[/tex]
3 = [tex]2^{1}\times2^{0.585}[/tex]
[tex]2^{0.585}=\frac{3}{2}[/tex]
[tex]2^{0.585}=1.5[/tex]
For x = 2.585,
f(2.585) = [tex]2^{2.585}[/tex]
= [tex]2^{2}\times 2^{0.585}[/tex]
= 4 × 1.5 [Since, [tex]2^{0.585}=1.5[/tex]]
= 6
From table 2,
g(x) = [tex]\text{log}_b(x)[/tex]
For x = 0.5,
g(0.5) = -1
-1 = [tex]\text{log}_b(0.5)[/tex]
b⁻¹ = 0.5
b = 2
For x = 2,
g(2) = 1
1 = [tex]\text{log}_2(2)[/tex]
For x = 6,
g(6) = 2.585
2.585 = [tex]\text{log}_2(6)[/tex]
2.585 = [tex]\text{log}_2(2\times 3)[/tex]
2.585 = [tex]\text{log}_2(2)+\text{log}_2(3)[/tex]
2.858 - 1 = [tex]\text{log}_2(3)[/tex]
[tex]\text{log}_2(3)=1.585[/tex]
For x = 3,
g(3) = [tex]\text{log}_2(3)[/tex]
g(3) = 1.585
