log5 (8y - 6) - log5 (y - 5) = log4 16

Answer 1

To solve this equation, we can use logarithm properties. First, we can simplify the equation using the properties of logarithms.

Using the property log a - log b = log (a/b), we have:

log5(8y - 6) - log5(y - 5) = log4(16)
log5[(8y - 6)/(y - 5)] = log4(16)

Now, we can convert the equation into exponential form. Recall that log a b = x is equivalent to b = a^x.

From the equation above, we have:

(8y - 6)/(y - 5) = 16^4

Simplifying the right side, we have:

(8y - 6)/(y - 5) = 2^8

Next, we can solve this equation for y by cross-multiplying:

2^8(y - 5) = 8y - 6

Expanding both sides, we get:

256y - 1280 = 8y - 6

Combining like terms, we have:

248y - 1274 = 0

Adding 1274 to both sides:

248y = 1274

Dividing both sides by 248:

y = 1274/248

Simplifying the fraction, we get:

y = 5.1371

Therefore, the solution to the equation is y = 5.1371.