You're just a bump on a LOG
What is the word that indicates the COMMON logarithm? And what is its base?
(Hint: it's one of the buttons on your calculator!)
"LOG", base 10
EXPAND the logarithm using the Law(s) of Logarithms:
\log_7(x^100)
100\log_7(x)
This is the equation for what?
A(t)=P(1+\frac{r}{n})^{nt}
Compound Interest
Solve for x:
\log_6(x)=5
x = 7,776
How would you turn an exponential equation into a logarithmic equation, and vice versa?
\text{base}^{\text{exponent}}=\text{result} \quad \leftrightarrow \quad \log_{\base}(\text{result})=\text{exponent}
What is the word that indicates the NATURAL logarithm? And what is its base?
(Hint: it's one of the buttons on your calculator!)
"LN", base e
COMBINE the logarithm using the Law(s) of Logarithms:
\ln(q)+\ln(t)+\ln(\pi)
\ln(qt\pi)
;)
What's the equation for exponential growth?
P(t)=P_0b^{kt}, where: b>1
Solve for x:
log_11(1/(161,051))=x
x = -5
Rewrite the following logarithmic equation into an exponential equation:
log_3(81)=4
3^4=81
Evaluate the logarithm:
\log_3(81)
4
COMBINE and SIMPLIFY the logarithm using the Law(s) of Logarithms:
ln(x)+ln(x-2)
ln(x^2-2x)
What are the corresponding values of n if interest is compounded annually, semiannually, quarterly, monthly, weekly, and daily?
Annually: n = 1
Semiannually: n = 2
Quarterly: n = 4
Monthly: n = 12
Weekly: n = 52
Daily: n = 365
Solve for x:
log_x(4,913)=3
x = 17
Rewrite the following exponential equation into a logarithmic equation:
625^{\frac{1}{2}}=25
log_{625}(25)=\frac{1}{2}
Evaluate the logarithm:
\log(\frac{1}{100})
-2
EXPAND and SIMPLIFY the logarithm using the Law(s) of Logarithms:
\log_7(\frac{a^2b^3}{c^5} )
2log_7(a)+3log_7(b) - 5log_7(c)
A lake has a frog population of 236 frogs, how many frogs will be in the lake in 2 years if the growth rate is 12%?
300 frogs
DAILY DOUBLE!
Solve for x:
log(x+10)+log(x-6)=2\log(x)
x = 15
Rewrite the following exponential equation into a logarithmic equation:
10^1=10
log(10)=1
Evaluate the logarithm:
\log_64(4)
\frac{1}{3}
EXPAND and SIMPLIFY the logarithm using the Law(s) of Logarithms:
\log_2(\sqrt{\frac{s}{rt}} \ )
\frac{1}{2}log_2(s)-\frac{1}{2}log_2(r) - \frac{1}{2}log_2(t)
Val makes a $7,000 investment at an interest rate of 8% that compounds quarterly. How much will the investment be after 3 years?
$8,877.69
Find the inverse function of:
f(x)=\frac{x^3+4}{5}
f^{-1}(x)= \ ^3\sqrt{5x-4}
Rewrite the following logarithmic equation into an exponential equation:
\ln(1)=0
e^0=1