Question

I'm having a hard time with log and ln and im being given the following problem:

log(x+7) + log(32x +4)=3

the problem is asking to solve for x.
is there a chance someone can explain to me the steps to solve the problem?

Answer 1

Rules of logs include the following:
log a + log b = log a*b (multiplication)
log a - log b = log a/b (division)
log a^b = b*log a (exponentiation).

Take your log (x+7) + log (32x + 4) and combine them into one log using the first rule listed above.

Answer 2

first use laws of logs to make one log

log (x+7)(32x + 4) = 3

i'm assuming these are logs to the base 10

so if log = 3 this means its the log of 10^3

so we have

(x + 7(32x + 4) = 10^3 = 1000

Answer 3

Actually, (x+7) * (32x + 4) = 1000.

How would you solve that for x?

Hint: multiply (x+7)*(32x+4) out first; then set the resulting product = to 1000 and solve that equation for x.

Answer 4

oh ok thank you guys. it's all very clear now