Answer:
x ≈ 0.18
Step-by-step explanation:
To solve the equation 10^(4x) = 72, we can take the logarithm of both sides of the equation. Since the base of the exponential term is 10, we can use the logarithm with base 10 (common logarithm) or the natural logarithm with base e (natural logarithm).
Let's use the natural logarithm (ln) in this case:
ln(10^(4x)) = ln(72)
Using the logarithmic property ln(a^b) = b * ln(a):
4x * ln(10) = ln(72)
Since ln(10) is a constant, we can substitute it with its approximate value:
4x * 2.3026 = ln(72)
Now we can solve for x:
4x = ln(72) / 2.3026
x = (ln(72) / 2.3026) / 4
x ≈ 0.7180 / 4
x ≈ 0.1795
Rounding to the nearest hundredth, x ≈ 0.18.
Therefore, the solution to the equation 10^(4x) = 72 is x ≈ 0.18.
