What is the solution of log((2x + 7))27 = 3?

Question

ranga · Answer

Is that (2x+7) raised to 27?  (Is 27 an exponent?)

anonymous · Answer

uhm the 2x+7 is like an exponent but lower not higher

ranga · Answer

Does it look like this?$$\Large \log_{(2x+7)} 27 = 3$$

anonymous · Answer

yes

ranga · Answer

$$\Large \log_{b} A = C$$means$$\Large A = b^{C} $$Can you take it from here?

anonymous · Answer

soo 27=2x+7^3?

ranga · Answer

Exactly. But you need to put parenthesis: 27=(2x+7)^3
Take the cube root on both sides.

anonymous · Answer

19683=2x+343
I got 9,670

anonymous · Answer

wait so just cube the 2x and 7?

anonymous · Answer

27=8x+343
-316
with that i got -39.5

ranga · Answer

No. Cube root of 27 is 3 because 27 = 3 x 3 x 3

Cube root of (2x+7)^3 is:  [ (2x+7)^3 ]^1/3.  The 3 and 1/3 will cancel out leaving you with just (2x+7)

So 2x + 7 = 3.  Solve for x

anonymous · Answer

-2

anonymous · Answer

thank you that's one of the answers!

ranga · Answer

Yes. That is the correct answer.  
You are welcome.