Question

Use a convert log to exponential calculator.

a) log₃(9) = x
b) 10^x = 100
c) ln(e^x) = 5
d) log₂(8) = 3

Answer 1

Question a: x = 2, Question b: x = 2, Question c: x = 5, Question d: x = 3.

Step-by-step explanation:

Question a:

To solve the equation log₃(9) = x for x, we have to rewrite it as an exponential equation. In this case, the base is 3, the logarithm of 9, and the exponent is x. So 3^x = 9. Therefore, x = 2.

Question b:

To find the value of x in the equation 10^x = 100, we rewrite it as a logarithmic equation. The base is 10, the exponent is x, and the logarithm of 100. So x = log₁₀(100). Evaluating this logarithm, we find that x = 2.

Question c:

The equation ln(e^x) = 5 represents the natural logarithm of e raised to the power of x and equals 5. We can simplify this equation by applying the inverse property of logarithms. The natural logarithm of e is 1, so we have x = 5.

Question d:

The equation log₂(8) = 3 is asking for the logarithm base 2 of 8, which equals 3. To solve it, we rewrite it as an exponential equation. The base is 2, the exponent is the logarithm of 8, and the result is 3. So 2^3 = 8, and x = 3.