SOLUTION: Hi, I'm unsure on how to solve this problem: {{{ 7^(2x) = 49^(3x+1) }}} Thank you so much to anyone who can help!

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Question 1016251: Hi,
I'm unsure on how to solve this problem:

Thank you so much to anyone who can help!
Found 3 solutions by Alan3354, ankor@dixie-net.com, Theo:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!

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Hint: 49 = 7^2

Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!

we know that 49 is 7^2 therefore we can write this

therefore
2x = 2(3x+1)
2x = 6x + 2
2x - 6x = 2
-4x = 2
x = 2/-4
x =
:
:
We can confirm this in the original equation, use -.5 for x

We know that an exponent of .5 means the square root, neg is the reciprocal
=

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
7^(2x) = 49^(3x+1)

one way to solve this is:

start with:

7^(2x) = 49^(3x+1)

since 49 = 7^2, this equation becomes:

7^(2x) = (7^2)^(3x+1)

this becomes 7^(2x) = 7^(2*(3x+1)) which becomes:

7^(2x) = 7^(6x + 2)

since the base is the same, you can just set the exponents equal to each other and solve for x.

you get 2x = 6x + 2

solve for x to get x = -1/2

another way to solve it is:

start with:

7^(2x) = 49^(3x+1)

take the log of both sides of the equation to get:

log(7^(2x) = log(49^(3x+1))

this becomes 2x * log(7) = (3x+1) * log(49)

since 49 is equal to 7^2, this becomes 2x * log(7) = (3x+1) * log(7^2).

this becomes 2x * log(7) = 2 * (3x + 1) * log(7) which becomes:

2x * log(7) = (6x + 2) * log(7)

if you divide both sides of this equation by log(7), you get:

2x = 6x + 2

solve for x to get x = -1/2

if you did not recognize that 49 = 7^2 and that you could then get 2 * log(7), you could still have solved as follows:

start with:

2x * log(7) = (3x+1) * log(49)

find log(7) and find log(49) and the equation becomes:

2x * .84509804 = (3x + 1) * 1.69019608

simplify to get:

1.69019608 * x = 3x * 1.69019608 + 1 * 1.69019608

this becomes 1.69019608 * x = 5.07058824 * x + 1.69019608

subtract 1.69019608 * x from both sides of the equation and subtract 1.69019608 from both sides of the equation to get:

-1.69019608 = 5.07058824 * x - 1.69019608 * x

combine like terms to get -1.69019608 = 3.38039216 * x

divide both sides of this equation by 3.38039216 and solve for x to get:

x = 3.38039216 / -1.69019608 = -.5 which is the same as -1/2.

it was a lot messier because of the arithmetic involved but you go the same answer.