Question 143989
I'll do the first two to get you started


# 1


{{{log(5,(4x))=log(5,(28))}}} Start with the given equation



{{{4x=28}}} Since the logs have the same base, this means that the arguments (the stuff inside the logs) are equal.



{{{x=(28)/(4)}}} Divide both sides by 4 to isolate x




{{{x=7}}} Divide


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Answer:

So our answer is {{{x=7}}} 



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# 2


{{{2log(10,(x))+ log(10,(3))=log(10,(48)) }}} Start with the given equation



{{{log(10,(x^2))+ log(10,(3))=log(10,(48)) }}} Rewrite {{{2log(10,(x))}}} as {{{log(10,(x^2))}}}



{{{log(10,(x^2*3))=log(10,(48)) }}} Combine the logs using the identity {{{log(b,(A))+log(b,(B))=log(b,(A*B))}}}



{{{log(10,(3x^2))=log(10,(48)) }}} Rearrange the terms



{{{3x^2=48}}} Since the logs have the same base, this means that the arguments (the stuff inside the logs) are equal



{{{x^2=16}}} Divide both sides by 3



{{{x=4}}} Take the square root of both sides. Note: discard the negative square root. Remember, you cannot take the log of a negative number.


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Answer:

So our answer is {{{x=4}}}