solve: 9^x = 1/27?

Question

please help me
i dont understand it

thanks

Answer 1

9^x = 27^(-1)
Take log base 3 of both sides:-
x log 9 = log 27^(-1)
x = (-1) log 27 / log 9
x = (-1) 3 / 2
x = - 3 / 2

Answer 2

You must use logarithms in order to solve this....Because if you use logs, then you can pull the exponent down in front of the x....There is also another rule with regard to logarithms, you need to understand this or you'll have so much trouble in the future...

9^x=1/27
log 9^x=log 1/27
x log 9=log 1/27 ---> The rule that I mentioned above
we can now divide both sides by log 9
x= (log 1/27)/(log9)

This is the same answer as provided by the first person to answer the question, his way is easier. However, it is fundamentally important that you understand this way as well.

Answer 3

Solving this sort of equation requires the use of logarithms.

Take the log of both sides to get:

log 9^x = log 1/27

Hence: x log 9 = log 1/27

x = [log 1/27]/log 9

using your calculator:

x = -1.5

You can use logs to the base 10 (Lg on your calculator) or logs to the base e (In on your calculator).

Answer 4

u first try to make the whole number the same since u have 9 & 27 as the whole numbers u wanna c what they have in common....

* they have 3 in common *


so u do this after that.....


3^ 2x = 3^-3

after this the like terms( or in this case the numbers will cancel out such as the whole numbers r the same so they cancel out.....it will look like this now.....


2x=-3

after this u will have to divide the -3 over the 2 to c wt x ='s.


2x/2 = -3/2

u will see that after dividing them u get x to = -3/2. if u wanna check if x does = -3/2 u just plug it in.......n c if wt u got is the same on the other side.....

Answer 5

x = log9(1/27)
x = log10(1/27)/log10(9) (base change rule)
= - 1.5

Check:
9 ^ -1.5
1/ 9^1.5
--- taking the denominator only as text entry sucks ---
9^1.5 = 9 * 9 ^.5
= 9 * sqrt(9)
= 9 * 3 = 27
so the solution 1/27 is correct.

Answer 6

Change both sides to base 3 and set set exponents equal:

9^x = 1/27

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

2x = -3

x = -3/2

that's it! :)

Answer 7

9^x=1/27
(3^2)x=3^-3
3^2x=3^-3
2x=-3
x=-3/2