Respuesta :
Answer:
The given expression [tex]5log_{b}y+6log_{b} x[/tex] can be written as a single logarithm as [tex]log_{b}(y^5x^6)[/tex]
Step-by-step explanation:
Consider the given expression,
[tex]5log_{b}y+6log_{b}x[/tex]
Using the property of logarithm, [tex]log_ax^n=nlog_ax[/tex]
Applying reverse of above property, given expression becomes,
[tex]5log_{b}y+6log_{b}x[/tex]
[tex]\Rightarrow log_{b}y^5+log_{b}x^6[/tex] ...(1)
Now again using the property of logarithm [tex]log_{a}xy=log_ax+log_ay[/tex]
(1) can be written as,
[tex] log_{b}y^5+log_{b}x^6[/tex]
[tex]\Rightarrow log_{b}(y^5x^6)[/tex]
Thus, the given expression [tex]5log_{b}y+6log_{b} x[/tex] can be written as a single logarithm as [tex]log_{b}(y^5x^6)[/tex]
