8^x = 16^x+2, x+2
-2=0
8^x =16^x+2, 2 x 8 = 16
log sub 5 (2x+3)=2
2(7/2)+3=2
log sub 5 (2x+3)=2
log sub 5 =11
The first and second lines make no sense whatsoever.
The last is even more confusing.
Watch
8^x = 16^(x+2)
8^x = 8^2(x+2)
x= 2x+4 solve for x.
On the next
log5 (2x+3)=2
2x+3=25
solve for x.
I think you need a tutor to help you study this: your work seems helter skelter and in need of organized thought. Discuss this with your mom quickly.
I apologize for the confusion caused by my previous response. It seems there was a misunderstanding in the interpretation of the equations you provided. Let's go through the correct steps to solve them:
1. 8^x = 16^(x+2)
Take the logarithm of both sides using the same base on both sides. Let's use the logarithm base 2 (log2) for simplicity:
log2(8^x) = log2(16^(x+2))
Apply the power rule of logarithms and simplify:
x * log2(8) = (x+2) * log2(16)
Since log2(8) = 3 and log2(16) = 4, substitute these values:
3x = 4(x+2)
Simplify the equation:
3x = 4x + 8
Rearrange and solve for x:
3x - 4x = 8
-x = 8
x = -8
2. log5(2x+3) = 2
Rewrite the equation in exponential form using base 5:
5^2 = 2x + 3
Simplify the equation:
25 = 2x + 3
Subtract 3 from both sides:
25 - 3 = 2x
22 = 2x
Divide both sides by 2:
x = 11
Please note that my previous response contained incorrect interpretations and calculations. I apologize for any confusion caused. It's always a good idea to double-check the steps when solving equations to ensure accuracy.