solve the logarithmic equation round to the nearest then-thousandth if necessary

Question

3 log 2x = 4

Answer 1

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.