Find x: {9}^{2x + 1 = {81}^(3x + 1)

QAmmunity.org

My account
Edit my Profile
Private messages
My favorites

Ask a Question
Questions
Tags
Categories
Ask a Question

Aamir Shahzad asked Oct 21, 2022

519,549 views

30 votes

Find x:

${9}^{2x + 1 = {81}^(3x + 1)$

Mathematics
high-school

Aamir Shahzad asked Oct 21, 2022

by Aamir Shahzad

2.6k points

0 Comments

Your comment on this question:

Email me at this address if a comment is added after mine:Email me if a comment is added after mine

Privacy: Your email address will only be used for sending these notifications.

Your answer

Email me at this address if my answer is selected or commented on:Email me if my answer is selected or commented on

Privacy: Your email address will only be used for sending these notifications.

1 Answer

21 votes

Answer:

x = - (1)/(4)

Explanation:

${9}^(2x + 1) = {81}^(3x + 1) \\ \\{3}^(2(2x + 1)) = {3}^(4(3x + 1)) \\ \\ {3}^(4x + 2) = {3}^(12x + 4) \\ bases \: are \: equal \: so \: exponents \: \\ will \: also \: be \: equal\\ \\ 4x + 2 = 12x + 4 \\ \\ 2 - 4 = 12x - 4x \\ \\ - 2 = 8x \\ \\ x = - (2)/(8)\\ \\ x = - (1)/(4)$