Exponent Rules
What do you do when you see 7^2*7^3?
Add the exponents; 7^5
Solve. 3^x-2=12
x=2.4
Rewrite the exponential equation into a log equation. 5^3=125
log5(125)=3
How do you expand when you see log(xy)?
logx+logy
Condense. log5-log2
log(5/2)
Provide an example of a situation in which you would multiply exponents.
(a^m)^n
Solve. 3^2x-3=4
x=.9
Rewrite the log equation into an exponential equation. log5(25)=2
5^2=25
Expand. log(3*4^5)
log4+5log4
Condense. 5log2-5log7
log(2/7)^5
What values contain a negative exponent?
Fractions
log(5x)=log(2x+9)
x=3
Rewrite the log equation into an exponential equation. log2(16)=4
2^4=16
Expand. log(xyz^2)
logx+logy+2logz
Condense. 2log3u+2log3a
log3(ua)^2
What do you do? (a^m/a^n)
Subtract the exponents
logx+log7=log37
x=37/7
Rewrite the exponential equation into a log equation. 5^5=3125.
log5(3125)=5
What do you do when you see logb(a)?
loga/logb
Condense. 9log3b+9log3d
log3(bd)^9
Solve. 4^-x+1*(1/4)^2x=8^2x
x=1/6
11^x-8-5=54
x=9.7
Rewrite the exponential equation into a log equation. 6^5=7776
log6(7776)=5
Expand. log(x/y^6)
logx-6logy
Condense. 4(log2x-logy)-(log7+4log5)
log(2x/y)^4/log(7*5)^4