Help urgently for a maths exponential equation just need a and b!!

Question 1

Help urgently for a maths exponential equation
just need a and b!!

Question 2

2a)

$\rightarrow \sf 2^(x+1) = 2^x + 4$

$\rightarrow \sf 2^(x+1) -2^x = 4$

$\rightarrow \sf 2^1 * 2^x -2^x = 2^2$

$\rightarrow \sf 2^x\left(2^1-1\right) = 2^2$

$\rightarrow \sf 2^x\left(1) = 2^2$

$\rightarrow \sf 2^x = 2^2$

$\rightarrow \sf x= 2$

2b)

$\rightarrow \sf 2^x + 2^(x - 2) = 5$

$\rightarrow \sf 2^x + 2^(x) / 2^2 = 5$

$\rightarrow \sf 2^x + (2^(x))/(2^2) = 5$

$\rightarrow \sf 2^x(1 + (1)/(4) ) = 5$

$\rightarrow \sf 2^x(1.25 ) = 5$

$\rightarrow \sf 2^x = 5 / 1.25$

$\rightarrow \sf 2^x =4$

$\rightarrow \sf 2^x =2^2$

$\rightarrow \sf x=2$

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