Solve the logarithmic equation for x.?

Question

a. log(x-4)=3
b. log3(2-x)=3

Answer 1

a) 10^3=x-4
x=1000+4=1004

b) l0^3=3(2-x)
10^3=6-3x
3x=6-1000=-994
x= - 331 1/3

Answer 2

For part a:

log(x-4) = 3

"Think 10 to the both sides"

So,

10^(log(x-4)) = 10^3

(x-4) = 1000
x = 1004


For part b, just think "3 to the both sides [if it's a base 3 log, not sure if that was multiplication]"

log3(2-x) = 3

3^(log3(2-x)) = 3^3

2-x = 27

-x = 25

x = -25

Answer 3

a. log(x-4)=3
take the inverse log of both sides & solve for x
(x-4)=10^3 =1000
x-4+4 =1000+4
x=1004

b. log3(2-x)=3 (is this log base 3 or log base 10?)

if base 3
log3(2-x)=3
take the inverse log
2-x = 3^3 =27
-x = 27-2 =25
x=-25

Answer 4

General advice: Practice how to convert from logarithmic form to exponential form.

For part (a), if there is no given base, then the default is base 10. Steps to convert to exponential form are as follows:
(1) The base of the log becomes the base of the exponent.
(2) The inside of the log becomes the answer.

Therefore, if we take log(x-4) = 3
The base of the log (10) is the base of the exponent.
The inside of the log (x-4) is the answer.
(What's remaining becomes the expontent)

10^3 = x - 4
1000 = x-4
x = 996

Try part b that way.

Answer 5

b. 3^3=2-x
x=2-9
x=-7