Question

Log9x=log9 5+log9 6

Answer 1

$log_9x=log_95+log_96\; ,\; \; ODZ:\; \; x>0\\\\log_9x=log_9(5\cdot 6)\\\\log_9x=log_930\\\\x=30$

Answer 2

To solve the equation log9x = log9 5 + log9 6, we can use the properties of logarithms.

According to the product rule of logarithms, loga (xy) = loga x + loga y.

Therefore, we can rewrite the equation as:

log9x = log9 (5 * 6)

Now we simplify the right side:

log9 (5 * 6) = log9 30

Therefore, the equation becomes:

log9x = log9 30

Since both sides of the equation have the same base (9), we can drop the logarithm base:

x = 30

So the solution to the equation log9x = log9 5 + log9 6 is x = 30.