3. Determine the value of \( x \) in each of the following: \( \begin{array}{lll}\text { a) } 2,6 \times 10^{x}=0,26 & \text { b) } 4,8 \times 10^{x}=4800 & \text { c) } 7 \times 10^{x}=7000000 \\ \text { d) } x \times 10^{4}=83000 & \text { e) } x \times 10^{2}=125000 & \text { f) } 19643000 \times 10^{-6}=x\end{array} \)

To determine the value of \( x \) for each equation, we can isolate \( x \) by rewriting the equations in terms of powers of ten. a) \( 2.6 \times 10^{x} = 0.26 \) To solve for \( x \): \[ 10^{x} = \frac{0.26}{2.6} = 0.1 = 10^{-1} \] Thus, \( x = -1 \). b) \( 4.8 \times 10^{x} = 4800 \) To solve for \( x \): \[ 10^{x} = \frac{4800}{4.8} = 1000 = 10^{3} \] Thus, \( x = 3 \). c) \( 7 \times 10^{x} = 7000000 \) To solve for \( x \): \[ 10^{x} = \frac{7000000}{7} = 1000000 = 10^{6} \] Thus, \( x = 6 \). d) \( x \times 10^{4} = 83000 \) To solve for \( x \): \[ x = \frac{83000}{10^{4}} = 8.3 \] e) \( x \times 10^{2} = 125000 \) To solve for \( x \): \[ x = \frac{125000}{10^{2}} = 1250 \] f) \( 19643000 \times 10^{-6} = x \) To simplify: \[ x = 19643000 \times 10^{-6} = 19.643 \] The final values are: a) \( x = -1 \) b) \( x = 3 \) c) \( x = 6 \) d) \( x = 8.3 \) e) \( x = 1250 \) f) \( x = 19.643 \)