Solve for x: log6x-log2=1

Answers

Answer 1

Answer: $log6x-log2=1;\ D:6x > 0\to x > 0\to x\in\mathbb{R^+}\n\nlog6x-log2=1\n\nlog\left(6x:2\right)=log10^1\n\n3x=10\ /:3\n\nx=(10)/(3)\n\nx=3(1)/(3)\in D$

$a > 0\ \wedge\ b > 0\ \wedge\ c > 0\ \wedge\ d\in\mathbb{R}\n\nlog_ab-log_ac=log_a(b:c)\n\nlog_ab=d\iff\ a^d=b\ \ (log_ab=log_aa^d)$

Answer 2

Answer: Log(6x/2)=1
Log(3x)=1
This is the same as saying 10^1=3x
10=3x
x=10/3 or 3 and 1/3

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A boat company charges a flat fee of $35.00 plus $7.25 per hour to rent a boat. Another company charges a fee of $29.00 plus $10.50 per hour to rent the same boat. PLEASE SHOW WORK.

Answers

35.00 + 7.25x = 29.00 + 10.50x

How do I solve a quadratic equation like this: x squared minus 9x = -14?

Answers

$x^2-9x=-14\n\nx^2-9x+14=0\n--------------------\n-9=-7+(-2)\n14=-7\cdot(-2)\n--------------------\n\nx^2-9x+14=(x-7)(x-2)\n\n(x-7)(x-2)=0\iff x-7=0\ or\ x-2=0\n\nx=7\ or\ x=2$

$x^2-9x+14=0\n\na=1;\ b=-9;\ c=14\n\n\Delta=b^2-4ac\n\n\Delta=(-9)^2-4\cdot1\cdot14=81-56=25\n\nx_1=(-b-\sqrt\Delta)/(2a)\to x_1=(9-√(25))/(2\cdot1)=(9-5)/(2)=(4)/(2)=2\n\nx_2=(-b+\sqrt\Delta)/(2a)\to x_2=(9+√(25))/(2\cdot1)=(9+5)/(2)=(14)/(2)=7$

Bring everything over to one side.
x² -9x=-14
x²-9x+14=0
Now it is an easy trinomial so you need to find two numbers that add up to -9 and multiply to equal 14. The two numbers are -7 and -2.
x²-9x+14=0
(x-7)(x-2)=0
x= 7 and 2

Please help me ......

Answers

For the first problem, when you see expression like that it just means to write it twice, then FOIL it.
(2x-6) (2x-6)
If you don't know what FOIL is let me know and I can further explain it!

This also applies for the second question!

Can anyone help me solve this math problem?