Respuesta :
Step 1
[tex]f(x)=ab^x[/tex]when x = 2, f(2) = 3
[tex]\begin{gathered} f(2)=ab^2 \\ ab^2\text{ = 3 ------------------------------ (1)} \end{gathered}[/tex]when x = 4, f(4) = 5
[tex]\begin{gathered} f(4)=ab^4 \\ ab^4\text{ = 5 ------------------------- (2)} \end{gathered}[/tex]Step 2: Solve equations 1 and 2 simultaneously to find the value of a and b.
[tex]\begin{gathered} \text{From equation 1, make b}^2\text{ subject of relation and substitute} \\ in\text{equation 2} \end{gathered}[/tex]Therefore
[tex]\begin{gathered} \text{From ab}^2\text{ = 3} \\ b^2\text{ = }\frac{3}{a} \end{gathered}[/tex][tex]\begin{gathered} \text{From equation 2} \\ ab^4\text{ = 5} \\ a\text{ x (}\frac{3}{a})^2\text{ = 5} \\ a\text{ x }\frac{9}{a^2}\text{ = 5} \\ \frac{9}{a}\text{ = 5} \\ \text{Cross multiply} \\ 5a\text{ = 9} \\ a\text{ = }\frac{9}{5} \end{gathered}[/tex]Step 3: Substitute a in equation 1 to find the value of b.
[tex]\begin{gathered} b^2\text{ = }\frac{3}{a} \\ b^2\text{ = 3 }\frac{.}{.}\text{ a} \\ b^2\text{ = 3 }\frac{.}{.}\text{ }\frac{9}{5} \\ b^2\text{ = 3 x }\frac{5}{9} \\ b^2\text{ = }\frac{5}{3} \\ \text{b = }\sqrt[]{\frac{5}{3}} \end{gathered}[/tex]Final answer
[tex]b\text{ = }\sqrt[]{\frac{5}{3}}[/tex]