To solve the given exponential equation, 10^x = 4.25, we will use logarithms. Logarithms are the inverses of exponential functions, and they will allow us to bring the variable x from the exponent down to a level where we can solve for it more easily.
Here are the steps we will follow:
1. Write the exponential equation: 10^x = 4.25;
2. Apply logarithm on both sides of the equation to get rid of the exponent for x on the left-hand side. Remembering that the logarithm of a number to its base is 1, we'll use base 10 logarithms (log) since the base in our equation is 10, so now the equation will be - log(10^x) = log(4.25);
3. Using the power rule for logarithms, which states that logb(m^n) = n * logb(m), where b is the base and m^n is the argument of the logarithm, we can pull down the x from the exponent in our case, so we get - x*log(10) = log(4.25);
4. Since the log(10) will be equal to 1 (since 10^1 = 10), the equation now simplifies down to x = log(4.25);
5. Now we solve for x by computing the base 10 log of 4.25;
6. After calculating (using a scientific calculator or logarithm table), the value of x in the equation becomes - x = 0.6283889300503115.
Therefore, the solution to the desired equation 10^x = 4.25 is x = 0.6283889300503115.