Answer :

Sure! Let's solve the equation step-by-step:

We start with the equation:

[tex]\[
\log_6 x + \log_6 9 = \log_6 5
\][/tex]

Using the properties of logarithms, we know that:

[tex]\[
\log_b a + \log_b c = \log_b (a \times c)
\][/tex]

So, we can combine the logarithms on the left side:

[tex]\[
\log_6 (x \times 9) = \log_6 5
\][/tex]

Since the logarithms on both sides have the same base, we can equate the arguments (what's inside the logs):

[tex]\[
x \times 9 = 5
\][/tex]

Now, solve for [tex]\( x \)[/tex] by dividing both sides by 9:

[tex]\[
x = \frac{5}{9}
\][/tex]

Therefore, the solution to the equation is:

[tex]\[
x = \frac{5}{9}
\][/tex]

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