Solve the unknown exponents by the law of logarithm correct to 5^2x+3=125.

Answer 1

Given equation:

5^(2x + 3) = 125

In order to solve for x, we need to rewrite the equation using logarithms.

Taking the logarithm of both sides, we get:

log(5^(2x + 3)) = log(125)

Using the property of logarithms that states log(a^b) = b*log(a), we can rewrite the left side of the equation as:

(2x + 3) * log(5) = log(125)

Now, we solve for x:

(2x + 3) * log(5) = log(125)
2x*log(5) + 3*log(5) = log(125)
2x*log(5) = log(125) - 3*log(5)
2x = (log(125) - 3*log(5)) / log(5)
x = (log(125) - 3*log(5)) / (2*log(5))

Solving this out will give you the value of x. You can use a calculator to get the numerical value.