Question

solve the exponential equation express the solution set in terms of natural logarithms 2^x+8=3

Answer 1

\[2^{x+8}=3\]

Answer 2

Well, you should apply the natural logarithm to both sides.

Answer 3

hint:
\[\ln a^x = x \ln a\]

Answer 4

still need more steps to figure it out

Answer 5

\[\ln 2^{x+8} = \ln 3\]

Answer 6

Can you continue?

Answer 7

no sorry still lost

Answer 8

Okay, you know that the logarithm of a power makes the power cones down? so the x+8 will come down in front of the ln2\[(x+8) \ln2 = \ln 3\]

Answer 9

yes ok I remember that

Answer 10

Can you solve for x?

Answer 11

do I distribute ln 2 to x+8

Answer 12

Nope, that would be a little tedious. Divide both sides by ln 2.

Answer 13

...natural log?

why not log to base 2


\[2^{x+8}=3\\
\log_2(2^{x+8})=\log_2(3)\\
(x+8)\log_2(2)=\log_2(3)\\
x+8=\log_2(3)\\
x = ... \]

Answer 14

@UnkleRhaukus Because the question requires the answer to be in terms of the `natural log`. So using log base 2 would require a change of base later on, seems tedious.

Answer 15

hmm, you are right, it is important to read the question properly,

Answer 16

@UnkleRhaukus I would have used base 2.

Answer 17

have to go I will workm on this later today