Answer to Question #193680 in Algebra for chris

Question #193680

1.Use log properties to condense:

a. log8x + log8p

b. logx1= 0


2.Rewrite into log form:

a. 5x = 25

b. 13/4 = 1/64


3.Solve 63x+5= 6x-2

1
Expert's answer
2021-05-17T17:04:51-0400

(1)

(a)For a part we will use the property

"log_a(x\\times y) = log_a(x) + log_a(y)"

So we have ,"log_8x + log_8(p) = log_8^{(x\\times p)}"  

"log_8^{(xp)}"


b) in second part it is already given 

This is the property of log that log(1) at any base is zero.

So 

"log_x(1) = 0"


(2)

To find log form

formula

"if \\space M^{n}=p"

then "n=log \\space M^{p}"

hence m is the base of the log

(a)

"5^{x} = 25"

"x=log _5^{25}"

hence base "=5"


(b)

"(\\frac{1}{4} )^{3}=\\frac{ 1}{64}"

"3=log(\\frac{1}{4})^\\frac{1}{64}"

hence base"=\\frac{1}{4}"


(3)

"if\\space a^x=a^{y} , \\space then\\space x=y"

hence given equation "6^{3x+5}= 6^{x-2}"

"3x+5=x-2"

"2x=-7"

"x=-\\frac{7}{2}"


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