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# Logarithms

### Logarithmic function and properties of logarithms

write as an exponential equation: log_3(9)=2 If b>0 and b#1, then y=log_b(x) means x=b^y b=3; x=9; y=2 9=3^2 is the answer
write as a logarithmic equation: 4^2=16 log_4(16)=2
write as a logarithmic equation: 2^-4=1/16 log_2(1/16)=-4
Find the value of the logarithmic expression: log_3(243) y=log_3(243) 3^y=243=3^5 y=5; then log_3(243)=5 is the answer
Solve: log_2(8)=x x=3
Solve the equation: log_16(x)=1/2 16^1/2=x x=4
Find the Value of the logarithmic expression 9^log_9(6) Remember: if b>0 and b#1, the b^log_b(x)=x 9^log_9(6)=6
Find the value of the logarithmic expression: log_4(4^3) log_4(4^3)=3log_4(4) log_4(4)=1, then log_4(4^3)=3 the answer is 3
write the sum as the logarithm of a single number: log_10(12)+log_10(11) log_10(132) Remember log_b(xy)=log_b(x)+log_b(y)
Solve the equation: log_3(4)+log_3(x)=0 x=1/4 Remember: log_3(4)+log_3(x)=log_3(4x)=0 3^0=4x=1 x=1/4
Solve the equation: log_10(x^2-9x)=1 x=(-1,10) x^-9x=10^1=10 x^2-9x-10=0 (x-10)(x+1)=0
Use the formula to solve the compound interest problem. A=P(1+r/n)^nt Find how long it takes for \$1300 to double if it is invested at 8% interest compounded monthly. The money will double in value in approximately t=8.7 years. Remember: P=\$1300, means A=\$2600, n=12 months, r=8% and t is what we are looking for.