SOLUTION: 1) Express loga X2 + 2 loga Square root of X as a single logarithm. Simplify if possible. 2) Given logb 2=0.387 and logb 5=0.898 find log square root of 20 3) solve 2x+3

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Question 38201: 1) Express loga X2 + 2 loga Square root of X as a single logarithm. Simplify if possible.
2) Given logb 2=0.387 and logb 5=0.898 find log square root of 20
3) solve 2x+3
5 =125
4)logx +log(x-2)=1

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1) Express loga X^2 + 2 loga Square root of X as a single logarithm. Simplify if possible.
=2logX + 2log a = 2log(Xa)
2) Given logb 2=0.387 and logb 5=0.898 find log square root of 20
log20 = log(4*5) = 2log2 + log5 = 2(0.387)+0.898=1.672

3) solve 2x+35 =125
2x=90
x=45
4)logx +log(x-2)=1
log[x(x-2)]=1
log[x^2-2x]=1
x^2-2x=10
x^2-2x-10=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=44 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4.3166247903554, -2.3166247903554. Here's your graph:

Cheers,
Stan H.