Final answer:
In this problem, 'log x = 0.2' means the base 10 raised to 0.2 equals 'x', which gives 'x' approximately as 1.58489. Then, 'e^x' means Euler's number raised to the power of 'x', so 'e^1.58489' gives us approximately 4.87. Therefore, 'e^x' is roughly 4.87 when 'log x' equals 0.2.
Step-by-step explanation:
To solve this problem, we need to understand the relationship between logs and exponents. The statement log x = 0.2 means that the base 10 raised to the power of 0.2 equals x, or in mathematical notation 10^0.2 = x. The value of x can be calculated using a scientific calculator and it would approximately be 1.58489 (rounded to five decimal places).
Given the value of x, we can then calculate e^x. This represents Euler's number (approximately 2.71828) raised to the power of x. So e^x = e^1.58489.
Again, using a scientific calculator, we can calculate the value of e^1.58489 to be approximately 4.87 (rounded to two decimal places). So, e^x = 4.87 when log x = 0.2.
Learn more about Logarithms and Exponents