Solve for P: 125^(3P-4) = √5

Published on August 26, 2024

Algebra

This problem involves solving for the value of P in the equation 125^(3P-4) = √5. The solution involves simplifying both sides of the equation, expressing them with the same base, and then equating the exponents to solve for P. The final answer is P = 25/18.

Question

Answer

Let’s solve this problem step by step:

The equation given is:
First, let’s simplify the right side:
Now our equation looks like:
We know that , so let’s rewrite the left side:
Using the power rule , we can simplify:
Simplify the exponent on the left side:
When the bases are the same, the exponents must be equal:
Add 12 to both sides:
Divide both sides by 9:

Therefore, the value of P is

or approximately 1.389.

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features

Related math solutions

Solving a Cubic Equation by Factoring

This problem involves solving the cubic equation 2x^3 + 2x^2 - 24x = 0 by factoring out the greatest common factor and then factoring the resulting quadratic expression.

Finding Intersections of Set A with Real, Rational, Integer, and Irrational Number Sets

Determine the intersections of the given set A containing square roots, pi, repeating decimals, and fractions with standard number systems such as R, Q, Z, I, and N.

Add Rational Expressions with the Same Denominator

Simplify x/(x − 7) + (4x − 1)/(x − 7) by adding the numerators and keeping the common denominator. The result is (5x − 1)/(x − 7), where x ≠ 7.

Solve 11 = 4x + 7: Two-Step Equation

Solve the two-step equation 11 = 4x + 7 by subtracting 7 from both sides, then dividing by 4. The solution is x = 1.

Algebraic Proof: Show That an Expression is Even

Prove algebraically that the expression n^2 - 2 - (n - 2)^2 is always an even number by expanding the brackets and factoring out a 2.

🔎 Explore All Shared Math Solutions