Question

loga5Rewrite log43++log4 73using properties of logarithms.3A. log, (335)B. loga (72.510)c. loga55D. loga(710 .52)Reset Selection

Answer 1

`log_43+(1)/(3)log_45+(1)/(3)log_47`

start by using the property of the logarithm that states

`n\ast log_ab=log_a(b^n)`

then, if we apply the property

`log_43+log_4(5^{(1)/(3)})+log_4(7^{(1)/(3)})`

since all logarithms have the same base we can apply the property

`log_a(b)+log_a(c)=log_a(b\ast c)`

apply the property

`log_4(3\ast5^{(1)/(3)}\ast7^{(1)/(3)})`

simplify the product and write the potency as a radical

`\begin{gathered} log_4(3\sqrt[3]{7\ast5}) \\ log_4(3\sqrt[3]{35}) \end{gathered}`