Log Help: log6(b2+2)+log62 = 2, log3(5x+5)-log3(x2-1) = 0,

[klongoria1]

What would it look like to solve this equation, steph by step? This problem was in a math lesson of mine in which I was taugth the Properties of Logarithms: the Product, Quotient, and Power properties.

log6(b2 + 2) + log62 = 2

And this one, the zero at the end is really throwing me off:

log3(5x+5) - log3(x2 - 1) = 0

Also, how do you solve these 2 problems, and what is the main difference?

Equation 1: log 2 + log x = log 3

Equation 2: log 2 + log x = 3

Thanks!!

[stapel_eliz]

Do you know what logs are, and what the log rules are?

[klongoria1]

I do, but I need help applying some of the rules.

[stapel_eliz]

I do, but I need help applying some of the rules.

1) log₆(b² + 2) + log₆(2) = 2

Use the "addition" log rule to combine the logs on the left-hand side. Then use The Relationship to convert the resulting log equation into the equivalent exponential form. Then solve the quadratic equation for the value(s) of b.

2) log₃(5x + 5) - log₃(x² - 1) = 0

Move one of the logs to the other side of the "equals" sign, equate the arguments, and then solve the resulting quadratic equation.

3) log(2) + log(x) = log(3)

Use the same log rule you used in (1) to combine the logs on the left-hand side. Then equate and solve, just as you did in (2). (For loads of worked examples of solving log equations, try here.)

4) log(2) + log(x) = 3

Use the same log rule you used in (1) and (3) to combine the logs on the left-hand side. Then convert, as you did in (2), to the equivalent exponential form, and solve the resulting linear equation.

If you get stuck on any of the above, please reply showing how far you have gotten. Thank you!

Note: I'm afraid I don't know what you mean by "the main difference"...?