Simplify 3(log2x)-4[logx-log(y-5)]?

log what.

Please i dont know if you mean log base 2 or log base 10 or log base e.

EDIT: Ok so you have log base 10. I will rewrite the term with the 10 in each logarithm just to make it clearer:

3(log 10 2x) - 4[log 10 x - log 10 (y-5)]

Ok lets first remember these logarithm laws:

ln a + ln b = ln (ab)

ln a - ln b = ln (a/b)

As well as this, as it may come in handy:

ln (a^b) = b * ln a

So :

3(log 10 2x) - 4[log 10 x - log 10 (y-5)]

First using log laws we can collect the double bracket terms, giving us:

3(log 10 2x) - 4[log 10 x/(y-5)]

Now on both terms we can put the 3 and 4 into the logarithm using the exponent law, giving us:

log 10 8x^3 - log 10 x^4/(y-5)^4

using the difference of log laws again we get:

log 10 8x^3 / (x^4/(y-5)^4

= log 10 8x^3 * ((y-5)^4 / x^4)

= log 10 (8(y-5)^4/x)

or in short notation:

log (8(y-5)^4/x)

Technically it would probably be clearer and more simple to express this as a difference of logarithms but you asked for it as a single logarithm, so here it is. Hope this helps.

Order of Operations Parentheses Exponents Multiply Divide Add Subtract Remember to Add and Subtract from Left to Right AND Multiply and Divide Left to Right. So, (5 + 4 x 2) - 3 x 2^3 First, is parentheses. When looking in parentheses, start the list over again, first thing now inside is to multiply, then add. (5 + 4 x 2) - 3 x 2^3 (5 + 8) -3 x 2^3 13 - 3 x 2^3 -----> now, next would be exponents. 13 - 3 x 8 -----> 2^3 is 8. Now, next is to multiply. 13 - 24 ----> only thing left is addition and subtraction. 13 - 24 = -11 -----> recall that when adding and subtracting, different signs you subtract and keep the sign of the bigger number. Therefore, your answer is negative 11.