Question

Solve for x if -2 = log(3x + 5)

Answer 1

Question #1: What is the base of this logarithm?

Answer 2

I was told if there isn't a base written out then it's 10

Answer 3

that's true. So let's assume that the base is 10.
Now, you have log(3x+5). How would you get rid of that log operator?
Note that whatever you do to the right side of your equation, you must do to the left.

Answer 4

Subtract 5?

Answer 5

to get rid of log base 10
you need to apply exponential to both sides
\[10^{-2}=10^{\log (3x+5)}\]

Answer 6

Personally, I would do this, first.

3x + 5 > 0

x > -5/3

This will help you to avoid errors in the future.

Answer 7

xapproachesinfinity ' s approach hinges on the fact that the log and exponential functions are inverses of one another.

Note that
\[10^{\log_{10}x }=x\]

Answer 8

So, what's the value of \[10^{\log_{10}(3x+5) }\]

Answer 9

???

Answer 10

but why would we do such thing to begin with!
the reason is that \[\log_a (a^n)=n\]
and also \[a^{\log_a(n)}=n\]
this is from inverse relation of log and exponential

Answer 11

I have no idea what the value of 10^log10(3x+5) would be

Answer 12

I would I find the value?

Answer 13

Two of us have explained that the log and the exponential functions are inverses of one another, and thus cancel each other out.

I gave you the example
\[10^{\log_{10}x }=x\]

Answer 14

The expo. fn. 10^x and log to the base 10 are inverse functions and thus cancel out.

What is the value of
\[10^{\log_{10}(3x+5) }?\]

Answer 15

So it equals 8?

Answer 16

\(\log\left((-1)^2\right) \ne 2\log(-1)\)

Answer 17

So is the value 8?

Answer 18

from what we said \[10^{\log_10 (3x+5)}=3x+5\]

Answer 19

so it becomes only \[10^{-2}=3x+5 \]

Answer 20

So would I find 10^-2, then solve for x?

Answer 21

\[10^{-2}=\frac{1}{100 }\]
so \[\frac{1}{100}=3x+5\]

Answer 22

solve for x , this is just a the usual linear equation you are used to

Answer 23

oh actually there a problem
@tkhunny has mentioned

Answer 24

What problem?

Answer 25

oh nevermind... thought there is was an issue in the domain of log (3x+5)

Answer 26

Okay. So in decimal form would x = -1.663333?

Answer 27

but don't worry about that, just proceed to solving the equation

Answer 28

yeah seems right to me
it preferable to right your answer as compact as possible
i meant use fractions. Don't use decimal unless asked to

Answer 29

write* instead of right sorry

Answer 30

Yeah. I'm not good at using fractions and don't know how to convert that to a fraction.

Answer 31

the fraction is -499/300

Answer 32

Alright. Thank you for all the help!

Answer 33

welcome

Answer 34

im perplexed to why @tkhunny mentioned x>-5/3

Answer 35

i mean i know for log x is defined for x>0 only
for this equation there is really nothing to be cautious about

Answer 36

There is ALWAYS the DOMAIN to be cautions about.