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4log4(10x)=41/2

10x=2

x=1/5

Step-by-step explanation:

The first problem involves applying the addition property

log64+log69=log6(4⋅9)=log636=log662=2

The next requires subtraction property

log3(P/Q)=log3P-log3Q=6-7=-1

The next will require a calculator but first we need to solve for x.  But how do we get x by itself?

Lets take the log base 10 (typically just written as 'log') of both sides

log(4x+2)=log(14)

Here we can apply the exponent property of logarithms

log(4x+2)=(x+2)log(4)=log(14)

now lets solve for x

x+2=log(14)/log(4)

x=log(14)/log(4)-2

Now we can calculate the logs using most scientific calculators.  You can do that...

The last problem starts by using the addition property again:

log42+log45x=1/2

log4(2⋅5x)=log4(10x)=1/2

To finish solving for x we have to remember that y=ax and y=logax are inverses.  So if we feed each side of the equation into the function f(x)=4x we'll get...

4log4(10x)=41/2

10x=2

x=1/5

correct me if im wrong