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)
(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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