solve the logarithmic equation round to the nearest then-thousandth if necessary
3 log 2x = 4
To solve the logarithmic equation 3 log(2x) = 4, we will first isolate the logarithm by dividing both sides of the equation by 3:
log(2x) = 4/3
Next, we will rewrite the equation in exponential form by converting the base 10 logarithm to an exponent:
10^(log(2x)) = 10^(4/3)
Now, we can simplify the left side of the equation, as 10^(log(2x)) = 2x:
2x = 10^(4/3)
To solve for x, we can write 10^(4/3) as the cube root of 10^4:
2x = (cube root of 10^4)
Calculating the cube root of 10^4, we find:
2x = 21.544
Dividing both sides of the equation by 2:
x = 10.772
Rounded to the nearest thousandth, x ≈ 10.772.