Exponents, collecting terms and log rules

Exponent rules: xaxb=

Exponent rules: xaxb=x(a+b) (xa)b=

Exponent rules: xaxb=x(a+b) (xa)b=xab xa/xb=

Exponent rules: xaxb=x(a+b) (xa)b=xab xa/xb=x(a-b) x0=

Exponent rules: xaxb=x(a+b) (xa)b=xab xa/xb=x(a-b) x0=1

Try it: 2324= (52)3= 34/32= 70=

Try it: 2324=2(3+4) (52)3=52∙3 34/32=3(4-2) 70=1

Try it: 2324=2(3+4)=27 (52)3=52∙3=56 34/32=3(4-2)=32 70=1

Try it: 2324=2(3+4)=27=128 (52)3=52∙3=56=15625 34/32=3(4-2)=32=9 70=1

The most common error: What is 33?

The most common error: What is 33? 33= 3 x 3 x 3… not 3+3+3 nor 3 x 3. By definition.

Fractional exponents. By definition; (x1/2) (x1/2) =

Fractional exponents. By definition; (x1/2) (x1/2) = (x1/2+1/2) = x1=x Therefore, (x1/2) = √x Fractional exponents are roots.

Fractional exponents. Try it. 16 1/2 = 27 1/3 = 8 2/3 = 32 3/5 = 27 1/3 = 8 2/3 = 32 3/5 = 125 4/3 =

Fractional exponents. Try it. 16 1/2 = 4 27 1/3 = 3 8 2/3 = 4 27 1/3 = 3 8 2/3 = 4 32 3/5 = 8 125 4/3 = 625

Collecting terms: (xaybzc)(xdyfzg)= xa+3xa+y+yb= Collect exponents to identical bases when multiplying (xaybzc)(xdyfzg)= Collect identical base to exponent terms when adding. xa+3xa+y+yb=

Collecting terms: (xaybzc)(xdyfzg)=xa+dyb+fzc+g xa+3xa+y+yb=4xa+y+yb Collect exponents to identical bases when multiplying (xaybzc)(xdyfzg)=xa+dyb+fzc+g Collect identical base to exponent terms when adding. xa+3xa+y+yb=4xa+y+yb

Try it (315372)(347351)= xy2+x2+y+2xy2= Collect exponents to identical bases when multiplying (315372)(347351)= Collect identical base to exponent terms when adding. xy2+x2+y+2xy2=

Try it (315372)(347351)=355475 xy2+x2+y+2xy2=3xy2+x2+y Collect exponents to identical bases when multiplying (315372)(347351)=355475 Collect identical base to exponent terms when adding. xy2+x2+y+2xy2=3xy2+x2+y

Try it (3x5372)(347y52)= x+x2+x+2x2= Collect exponents to identical bases when multiplying (3x5372)(347y52)= Collect identical base to exponent terms when adding. x+x2+x+2x2=

Try it (3x5372)(347y52)=3x+4557y+2 x+x2+x+2x2=2x+3x2 Collect exponents to identical bases when multiplying (3x5372)(347y52)=3x+4557y+2 Collect identical base to exponent terms when adding. x+x2+x+2x2=2x+3x2

It is used to find the exponent Log rules. The log function is a function that states an exponent. If ab=c then loga(c)=b It is used to find the exponent

3 5 = 125 log ( 25 )= 2 The exponent The base

log and ln (that’s “ell-en”) There are two log buttons on your calculator and They use different bases (10 and e), but they can both do the job. To raise a number to an exponent, use the button. log ln ^ If you need to check—look at the inverse (2nd) functions

To find a log of any other base (not 10 or e) loga(b)=log10(b)/log10(a) and loga(b)=ln(b)/ln(a)

For example: log4(64)=log10(64)/log10(4) and log5(625)=ln(625)/ln(5)

Rules of logs: Without a calculator! log (ab) = Based on the rules of exponents!

Rules of logs: Without a calculator! log (ab) = log(a) + log(b) log (a/b) = Based on the rules of exponents!

Rules of logs: Without a calculator! log (ab) = log(a) + log(b) log (a/b) = log(a) - log(b) log (ab) = Based on the rules of exponents!

Rules of logs: Without a calculator! log (ab) = log(a) + log(b) log (a/b) = log(a) - log(b) log (ab) = b log (a) log (1/a) = Based on the rules of exponents!

Rules of logs: Without a calculator! log (ab) = log(a) + log(b) log (a/b) = log(a) - log(b) log (ab) = b log (a) log (1/a) = - log (a) Based on the rules of exponents!

Rules of logs: Without a calculator! log (ab) = log(a) + log(b) log (a/b) = log(a) - log(b) log (ab) = b log (a) log (1/a) = - log (a) …and log 1 = 0 in any base. Based on the rules of exponents!

Log equations Remember: the log is the exponent. Do a little algebra, rewrite as an exponent, solve.

ln x = 3.2

5(x+3) -4 =75

3 + log4 x =24

Write as a single log expression: log (3) +log (x)+2log(y)-4(log (z)+2log(x))

Write as a single log expression: