5^(2x+1) = 2^(4x-3)?

Question

How would you solve that? ^

Thanks.

Answer 1

5^(2x+1) = 2^(4x-3)
log 5^(2x+1) = log 2^(4x-3)
(2x+1)log5 =(4x-3)log2
(2x+1)/(4x-3) = log2/log5 = .43067
2x+1= .43067(4x-3) = 1.72268x - 1.29201
.27732x = -2.29201
x = - 8.26

Answer 2

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

Take logs of both sides

So (2x+1)log5 = (4x-3) log2

so 2x log5 - 4x log2 = -3log2-log5

So x(2log5 - 4 log 2)= -3log2-log5

ie x = - { 3log2 + log5}/(2log5 - 4 log 2)

So by calculator x ≈ - 2.703194

Answer 3

5^(2x+1)=2^(4x-3)
Apply log on both sides.
(2x+1) log5 = (4x-3) log2
2x log5 +log5 = 4x log2 -3log2
2x log5 -4x log2 = -3log2-log5
x ( 2 log5 - 4 log2 ) = -3log2 - log5
x = -3log2 - log5/ 2log5-4log2
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Answer 4

Take natural log of both sides:
(2x+1)ln[5] = (4x-3)ln[2]
2x ln[5] + ln[5] = 4x ln[2] - 3 ln[2]
x(4ln[2] - 2ln[5]) = ln[5] - 3 ln[2]
x = {ln[5] - 3 ln[2]}/{4 ln[2] - 2 ln[5]}

Answer 5

um there are two ways that i can think of but i am not sure which way you learned it
i highly doubt that those binomials are raised to a power of 5 and two but if they are, you will have to do FOIL mutliple times
otherwise if its the way i think which is distributive then you distribute the powers to the binomials and it would look like this
10x + 5 = 8x - 6
-8x -5 -8x - 5
2x=-11
x=-5.5
hope this helps

Answer 6

i dunno... btw i hate pi :)