To convert the exponential equation 2x = 8 into its logarithmic form, we need to understand the relationship between the two forms. An exponential equation is typically represented as ab = c, which can be rewritten in logarithmic form as loga(c) = b. In this case, we have the following:
1. Identify the base (a), which is 2.
2. Identify the result (c), which is 8.
3. Identify the exponent (b), which is x.
Now we need to express this relationship in logarithms. Since we want the base to be 10, we can denote the logarithmic form as:
log10(8) = x
This means that the logarithm of 8 in base 10 is equal to x. To find the numerical value of x, you can use a calculator or logarithm table to calculate this value:
x ≈ 0.903
In conclusion, the logarithmic form of the exponential equation 2x = 8 in base 10 is:
log10(8) = x, and the approximate value of x is 0.903.