Final answer:
To solve the equation 5x = 625 without knowing a power of 5 that equals 625, you can use logarithms. The logarithm base 5 of 625 can be written as log5(625). This can be solved by using a base change formula, which states that loga(b) = logc(b)/logc(a).
Step-by-step explanation:
To solve the equation 5x = 625 without knowing a power of 5 that equals 625, we can use the concept of logarithms. The logarithm base 5 of 625 can be written as log5(625). This can be solved by using a base change formula, which states that loga(b) = logc(b)/logc(a). In this case, we can use the common logarithm, which has a base of 10, to find the solution. The equation becomes log10(625)/log10(5), which simplifies to 2/log10(5). You can calculate this using a calculator to find the solution.