Question

Someone help to explain this please!!

log x + log (x + 48) = 2

Answer 1

well using log laws for multiplication the problem can be written as

\[\log(x(x + 48)) = 2~~~or~~~~\log(x^2 + 48x) = 2\]

if this is a base 10 log system them raise each side of the equation to a power of 10

and you need to know the log law

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

so

\[10^{\log(x^2 + 48x)} = 10^2\]

which becomes

\[x^2 + 48x = 100\]

now you can solve for x

and remember you can't take the log of a negative number when you consider the solutions.

Answer 2

@Hero no, I think I got it.

Answer 3

@campbell_st , so does x=4.9? I did square root to both sides, then added the x and got 49, then divided by 10.

Answer 4

well I would rewrite it as

\[x^2 + 48x - 100 = 0\]

and this factors to

(x - 2)(x + 50) = 0

so the solutions seem to be

x = 2 and x = -50

Answer 5

oh, I didn't know it was supposed to be written that way.

Answer 6

well lets look at the positive value x = 2

you get

log(2) + log(2 + 48)

this can be rewritten as

log(2 x 50) = log(100)

and 100 = 10^2

so it seems to make sense

Answer 7

oh ok, Thank you!