Problem
Simplify. Enter the result as a single logarithm with a coefficient of 1 . To enter the log, click in the answer cell, then click on the small yellow arrow on the right. Then click the Functions tab to access the log. If needed, you can change the base. Using the keyboard, you can also enter $\log _{3}\left(5 x^{4}\right)$ as $\log _{-} 3\left(5 x^{\wedge} 4\right)$. \[ \begin{array}{l} \log _{5}\left(2 x^{9}\right)+\log _{5}\left(5 x^{2}\right) \\ = \end{array} \] Question Help: $\square$ Video $\square$ Message instructor D Post to forum Submit Question
Solution
Step 1 ：The problem is asking to simplify the expression \(\log _{5}\left(2 x^{9}\right)+\log _{5}\left(5 x^{2}\right)\) into a single logarithm with a coefficient of 1.
Step 2 ：From the properties of logarithms, we know that the sum of two logarithms with the same base is equal to the logarithm of the product of the numbers.
Step 3 ：So, we can simplify the expression by multiplying the numbers inside the logarithms.
Step 4 ：The simplified expression is \(\boxed{\log _{5}\left(10 x^{11}\right)}\).
