Question

Algebra 2 help and explanation? I get confused when the base of the log isn't 10.

Solve the equation and round to the nearest ten-thousandth.

log2 4x = 5
(2 is the base)

Answer 1

And I need help with
2 log3 x = 54

Answer 2

\[log_2{4x} = 5\]
Raise both sides to the 5th power of the log base to get rid of the log:
\[4x = 2^5\]
\[x= 32/4 = 8\]
Check our work:

\[log_2{(4*8)} = 5\]
\[2^5 = 32 = 4*8\]

Remember the logarithm base n of x is just the number to which you raise n to get x.
So, the log base 2 of 32 is 5, because 2^5 = 32.

Answer 3

\[2\log_3 x = 54\]
I'd divide both sides by 2 to get
\[\log_3 x = 27\]
Can you tell me what x is now?

Answer 4

Or is the equation \[2\log{(3x)}=54\]?

Answer 5

I'm suspicious that the second problem isn't correct...

Answer 6

@whpalmer4 thanks so much! The second one has a base of 3.

Answer 7

for the second one I changed it to
log3 x^2 = 54
and then
3^54 = x^2
3^27 = x
x = 7.625 times 10^12

Answer 8

I would check your rounding carefully on that last one, you've gotten the right number, it would be a shame to still get it wrong (I'm not taking a position either way)

Answer 9

it would be

Answer 10

and so the answer is 8 if you solve for x