What is the solution of 7^3x=400?

Answer 1

To solve for x in the equation 7^(3x) = 400, we can take the natural logarithm of both sides:

ln(7^(3x)) = ln(400)

Using the property of logarithms that ln(a^b) = b*ln(a), we can simplify the left side:

3x*ln(7) = ln(400)

Now, divide both sides by ln(7) to solve for x:

3x = ln(400) / ln(7)
x = ln(400) / (3*ln(7))

Using a calculator to find the logarithms, we get:

ln(400) ≈ 5.9915
ln(7) ≈ 1.9459

Therefore,

x ≈ 5.9915 / (3*1.9459)
x ≈ 1.0243

So, the solution to the equation 7^(3x) = 400 is approximately x ≈ 1.0243.