Final answer:
To find the value of x in the equation 2 × 10^(4x) = 8, divide both sides by 2 to get 10^(4x) = 4, take the common logarithm of both sides to get 4x × log(10) = log(4), and then solve for x to obtain x = log(4) / 4.
Step-by-step explanation:
To find the value of x in the equation 2 × 10^(4x) = 8, we need to isolate x. First, we divide both sides of the equation by 2, which gives us 10^(4x) = 4. We then use a logarithmic expression to solve for x. By applying the common logarithm (base 10) to both sides, we create the equation log(10^(4x)) = log(4).
Using the property of logarithms that states the logarithm of a power is the exponent times the logarithm of the base, we can simplify it to 4x × log(10) = log(4). Since log(10) is equal to 1, the equation simplifies to 4x = log(4). Finally, to solve for x, divide both sides by 4, which gives us x = log(4) / 4. Thus, the logarithmic expression to find the value of x is x = log(4) / 4.