Question

2^3x-4=5 round to the nearest ten thousandth

Answer 1

the x is not part of the exponent correct?

Answer 2

it is

Answer 3

\[\huge\color{blue}{ 2^{3x}-4=5 } \]

Answer 4

is the 3x the exponent?

Answer 5

Add 4 to both sides, and hit both sides with a log.

Answer 6

ok

Answer 7

\[\huge\color{blue}{ 2^{3x}-~4~=~5 } \]\[\huge\color{blue}{ 2^{3x}-~4~\huge\color{red}{ +~4 } ~=~5 \huge\color{red}{ ~+~4 } } \]\[\huge\color{blue}{ 2^{3x} ~=~9 }\]\[\huge\color{blue}{ Log(2^{3x}) ~=~Log(9) }\]

Answer 8

\[\huge\color{blue}{ 3x~Log(2) ~=~Log(9) }\]
\[\huge\color{blue}{ 3x~Log(2) \color{red} { \div Log (2) }~=~Log(9) }\color{red} { \div Log (2) }\]
\[\huge\color{blue}{ 3x=~Log(9) }\color{blue} { \div Log (2) }\]
\[\huge\color{blue}{ 3x=~Log_2(9) }\]
\[\huge\color{blue}{ x=~Log_2(9) \div 3}\]
\[\huge\color{blue}{ x=~Log_2(9) \div Log_2(6)}\]
\[\huge\color{blue}{ x=~Log_6(9)}\]

Answer 9

Actually, I am not sure about the very last step.

Answer 10

ok

Answer 11

Yeah, the last step is correct, I just verified it.

Answer 12

http://www.1728.org/logrithm.htm

Answer 13

calculate the log when you need,

where it says "logarithm of" on 1 space to the right put the number the log of which you are taking
where it says "number base" put in the next space to the right, the base of the log. (if not specified which base, put 10)