use properties of logarithms to condense the logarithmic expression. write the expression as a single…

use properties of logarithms to condense the logarithmic expression. write the expression as a single logarithm whose coefficient is 1. evaluate logarithmic expressions if possible. \n$4\\log_{b}x + 7\\log_{b}z$\n$4\\log_{b}x + 7\\log_{b}z = \\square$

use properties of logarithms to condense the logarithmic expression. write the expression as a single logarithm whose coefficient is 1. evaluate logarithmic expressions if possible. \n$4\\log_{b}x + 7\\log_{b}z$\n$4\\log_{b}x + 7\\log_{b}z = \\square$

Answer

Answer:

$\log_b(x^4 z^7)$

Explanation:

Step1: Apply power rule

$4\log_b x = \log_b x^4$, $7\log_b z = \log_b z^7$

Step2: Apply product rule

$\log_b x^4 + \log_b z^7 = \log_b(x^4 z^7)$