Question

Solve the equation for x.

16 ^ (x - 7) + 5 = 24

x = log_24(16) + 7

x = log_5(7) + 24

x = log_19(16) + 7

x = log_16(19) + 7

Answer 1

The value of x is log16(19) + 7.

Therefore, the correct answer is: option "x = log_16(19) + 7".

Step-by-step explanation:

To solve the equation 16^(x - 7) + 5 = 24, we can start by subtracting 5 from both sides to isolate the exponent term: 16^(x-7) = 19.

To solve for x, we can take the logarithm of both sides using logarithm properties.

Taking the logarithm base 16 of both sides gives us:

log16(16^(x-7)) = log16(19).

Applying the logarithm property x logb(a) = logb(a^x), we have:

(x-7)log16(16) = log16(19).

Since the logarithm base 16 of 16 is 1, we have:

x-7 = log16(19).

Finally, we can solve for x by adding 7 to both sides: x = log16(19) + 7.