Solve 10^6x = 93. Round to the nearest ten-thousandth.
(1 point)
Responses
11.8109
1.0986
13.3801
0.3281
To solve the equation 10^(6x) = 93, we need to take the logarithm of both sides with base 10.
log(10^(6x)) = log(93)
Applying the power rule of logarithms, the exponent 6x can be brought down as a coefficient:
6x * log(10) = log(93)
Since log(10) = 1, the equation simplifies to:
6x = log(93)
To find the value of x, we divide both sides by 6:
x = log(93)/6
Using a calculator, we find that log(93) ≈ 1.9685.
Therefore, x ≈ 1.9685/6 ≈ 0.3281.
Rounding to the nearest ten-thousandth, x ≈ 0.3281.
So the correct answer is 0.3281.