Question

solve the given logarithmic or exponential equation.
1. log_27 x=-2/3

2. log_5 (x+9)-log_5 x=3

can someone include the work? i want to know how to solve these question by myself :)

Answer 1

for 1.
use the definition of log
\(\huge \log_ab=c \implies b = a^c \)

Answer 2

for 2. , use this property first
\(\large \log_ab-\log_ac =\log_a (b/c)\)
for the left part.

Answer 3

for i got no answer.
1. 1=-2/3log(27)
2. 1≠2/3log(27)
3. no solution

is that right?

Answer 4

\(\huge \log_ab=c \implies b = a^c \\ \huge \log_{27}x= -2/3 \implies x= 27^{-2/3}\)

can you simplify the right side ?

Answer 5

x=1/9

Answer 6

thats correct! :)

Answer 7

for the left side of 2nd., use this property
\(\large \log_ab-\log_ac =\log_a (b/c)\)

Answer 8

how do i set that up?

Answer 9

\(\large \log_ab-\log_ac =\log_a (b/c) \\ \large \log_5 (x+9)-
\log_5 x = ... ?\)

Answer 10

oh ok. i got 5^(x-1)

Answer 11

is that right?

Answer 12

where does x-1 come from ?

Answer 13

oh is it just 5?

Answer 14

wait... should the answer be 9?

Answer 15

see if you can understand that