I have 2 problems I need help with both I have narrowed it down to 2 possible answers but can't decide which one is right. The first problem log subscript 5 (2x+3)=2 the choices a)13/2 and b) 14. The next problem 8^x = 16^x+2 the choices a)8 and b)-8. Help please!

If log5 z = 2 then z=25
2x+3=25 x=you do it.

8^x = 16^(x+2)
8^x = 2^x+2 * 8^x+2
divide by 8^x

1=64*2^(x+2)
1/64 = 2^(x+2)
1/2^6 = 2^(x+2)
2^-6 = 2^(x+2)
now take the log base 2 of each side.

To solve the first problem, you have the equation log subscript 5 (2x+3) = 2. The choices are a) 13/2 and b) 14.

To find the value of x, we need to first convert the logarithmic equation into an exponential equation. Recall that if log5 z = 2, then z = 5^2, which is 25.

So, in this case, we have log subscript 5 (2x+3) = 2. This means that (2x+3) = 5^2, which is 25. Solving this equation, you get:

2x + 3 = 25
Subtracting 3 from both sides:
2x = 22
Dividing by 2:
x = 11.

Therefore, the correct answer for the first problem is not among the choices given (a) 13/2 and b) 14), but instead, x = 11.

Moving on to the second problem: 8^x = 16^(x+2). The choices are a) 8 and b) -8.

To solve this equation, we can simplify it by expressing 16 as 2^4 since both bases are powers of 2.

So, we have 8^x = (2^4)^(x+2), which simplifies to:
8^x = 2^(4(x+2)).

Next, we can convert both sides to have the same base, which is 2. Recall that 8 is equal to 2^3.

So, we have (2^3)^x = 2^(4(x+2)).

Using the properties of exponents, we can simplify this to:
2^(3x) = 2^(4(x+2)).

Since the bases are the same, the exponents must be equal. Therefore, we have:
3x = 4(x+2).

Expanding the equation, we get:
3x = 4x + 8.

Subtracting 4x from both sides, we have:
-x = 8.

Finally, multiplying both sides by -1, you get:
x = -8.

Therefore, the correct answer for the second problem is b) -8.