83.6k views
5 votes
Given the exponential equation:, find a common base and solve for x.

Given the exponential equation:, find a common base and solve for x.-example-1
User Mahbub
by
7.8k points

1 Answer

6 votes

Step-by-step explanation:

Given;

We are given the exponential equation shown below;


((125)/(8))^(4x-1)=((4^2)/(25^2))^(x+1)

Required;

We are required to

(i) Find a common base

(ii) Solve for x

Step by step solution;

To solve this problem we shall start with the following steps;


[((5)/(2))^3]^(4x-1)=[((2)/(5))^4]^(x+1)

For the left side of the equation, we can refine by applying the rule of exponents;


\begin{gathered} Flip\text{ the left side of the equation:} \\ ((2)/(5))^(-3) \end{gathered}

Therefore, we now have;


[((2)/(5))^(-3)]^(4x-1)=[((2)/(5))^4]^(x+1)
((2)/(5))^(-12x+3)=((2)/(5))^(4x+4)

We now have a common base and that means;


\begin{gathered} If: \\ a^x=a^y \\ Then: \\ x=y \end{gathered}

Therefore;


-12x+3=4x+4
-12x-4x=4-3
-16x=1

Divide both sides by -16;


x=-(1)/(16)

ANSWER:


x=-(1)/(16)

User AizuddinAzman
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories