Question

How do I solve these?
log5x + log4 = 3

Answer 1

Have you ever attempted to solve logs before?

Answer 2

do you know the log rules?

Answer 3

\[\log(a)+\log(b)=\log(ab)\]

you have log(5x) you can seperate this

Answer 4

We just started learning them this week and at first we were just doing the basic log rearranging of them, but I'm so lost with this. I think I missed something.

Answer 5

\[\log(a)-\log(b)=\log(a/b)\]

Answer 6

I don't understand. Do I plug the numbers into that? or?

Answer 7

okay so if I have
\[\log(4)+\log(x)=\log(4x)\]
then it is okay to say I can split up log(4x)
\[\log(4x)=\log(4)+\log(x)\]

so if you seperate
log(5x)

then solve your given expression to get it in the form of
log(x)=....

try this then I will help you from here

Answer 8

log4 = 5x + 3?

Answer 9

no

Answer 10

log(5x)=log(5)+log(x)

so replace it

Answer 11

log(5)+log(x)+log(4)=3

Answer 12

now use your rule for log(a)+log(b)=log(ab)

Answer 13

Oh okay sorry

Answer 14

\[\log(5)+\log(4)=\log(5 \times 4)\]

Answer 15

replace it

Answer 16

log(x)+log(20)=3

Answer 17

now re arrange it to get log(x)=... can you do this?

Answer 18

log(20x)=3?

Answer 19

okay if you wanna do it that way sure

Answer 20

now I need to know, if we are in base 10 or natural log

Answer 21

In base 10

Answer 22

now I need to know, if we are in base 10 or natural log

Answer 23

Do you understand the rules of exponents?

Answer 24

okay i am getting some serious issues with this website one sec

Answer 25

Wio no I don't understand them that well

Answer 26

\[\log_{a}(b)=Y\]
\[a^{Y}=b\]

Answer 27

You can leverage your own understanding of exponents to do logarithms. \[
\log5x + \log4 = 3\\
10^{\log 5x+\log 4}=10^3\\
10^{\log 5x}\cdot10^{\log 4} = 1000\\
(5x)(4) = 1000
\]

Answer 28

@wio can you finish this? I am having some issues

Answer 29

However, in this case, just using logarithm properties are just good, since you're not familiar with either.

Answer 30

log(20x)=3

since we are already this far you know the base is 10
and since I posted the rule for the log where you do the base raised to the power of the answer

so in this case
10^3=20x

then solve for x

Answer 31

The exponent property: \[
x^a\cdot x^b=x^{a+b}
\]Corresponds to the logarithm property: \[
\log(a)+\log(b) = \log(a\cdot b)
\]

Answer 32

x=50?

Answer 33

that's it

Answer 34

yes, also numerical solution via tool is 50 :)

http://www.equationcalculator.org/?input=log+%285x%29+%2B+log+%284%29+%3D+3&submit=Calculate

Answer 35

Thank you guys :)