Answer:
Question 5. [tex]a=2[/tex]
Question 6. [tex]d=4[/tex]
Step-by-step explanation:
Question 5.
Given:
[tex]\frac{3^{a}2\sqrt{9}}{27\sqrt{4}} = 1[/tex]
Solution:
[tex]\frac{3^{a}2\sqrt{9}}{27\sqrt{4}} = 1[/tex]
[tex]3^{a} 2\sqrt{9} =27\sqrt{4}[/tex]
[tex]3^{a} =\frac{27\sqrt{4} }{2\sqrt{9} }[/tex]
[tex]3^{a}=\frac{27\sqrt{2^{2} } }{2\sqrt{3^{2} } }[/tex]
[tex]3^{a}=\frac{27\times 2}{2\times 3}[/tex]
[tex]3^{a}=\frac{27}{3}[/tex]
[tex]3^{a}=9[/tex]
[tex]3^{a}=3^{2}[/tex]
Take log both side.
[tex]log(3)^{a} =log(3)^{2}[/tex]
Simplify th above equation.
[tex]a\times log(3)=2\times log(3)[/tex]
log(3) cancelled both side
[tex]a=2[/tex]
Question 6.
Given:
[tex]\frac{3^{d}\sqrt{5}}{3^{2}\sqrt{45}} = 3[/tex]
Solution:
[tex]\frac{3^{d}\sqrt{5}}{3^{2}\sqrt{45}} = 3[/tex]
[tex]3^{d}\sqrt{5} =3\times 9\sqrt{45}[/tex]
[tex]3^{d} =\frac{27\sqrt{45} }{\sqrt{5} }[/tex]
[tex]3^{d} =27\sqrt{\frac{45}{5}}[/tex]
[tex]3^{d} =27\times \sqrt{9}[/tex]
[tex]3^{d} =27\times \sqrt{3^{2}}[/tex]
[tex]3^{d} =27\times 3[/tex]
[tex]3^{d} =81[/tex]
[tex]3^{d}=3^{4}[/tex]
Take log both side.
[tex]log(3)^{d} =log(3)^{4}[/tex]
Simplify the above equation.
[tex]d\times log(3)=4\times log(3)[/tex]
log(3) cancelled both side
[tex]d=4[/tex]
Therefore [tex]a=2[/tex] for question 5 and [tex]d=4[/tex] for question 6.
