Question

1.Use log properties to condense:

a. log₈x + log8p

b. log_x1= 0

2.Rewrite into log form:

a. 5^x = 25

b. 1³/4 = 1/64

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

Answer 1

(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 $6^{3x+5}= 6^{x-2}$

$3x+5=x-2$

$2x=-7$

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