Question

What is the solution to the equation below? log 20x3 - 2log x=4

Answer 1

Answer:

x=500

Step-by-step explanation:

To solve the equation given, we will follow the steps below:

log 20x³ - 2log x=4

using the law of logarithm,

2log x = log x²

so, our equation becomes;

log 20x³ - log x²=4

Also using another law of logarithm;

log 20x³ - log x² = log (20x³/x²)

our equation becomes;

log (20x³/x²) = 4

log 20x = 4

from the definition of logarithm, logarithm is the power of the exponential

10⁴ = 20 x

10000 = 20x

divide both-side of the equation by 20

10000/20 = 20x/20

at the right-hand side of the equation 20 will cancel-out 20 leaving us with just x  and the left-hand side of the equation, 10000 will be divided by 20

500 = x

x = 500