Logs + logging Exponential equations

Resources recommended: TI 84 calculator (can be found online)

How do you log with a base in the TI 84 calculator?

MATH then scroll down to A:logBASE:

Logging is the opposite of what?

Exponents. Basically asking to what power must we raise this number to get the given number? EX:

Log_a1=?

0

Log_aa=?

1

Log_a(mn)=?

Log_a(m)+Log_a(n)

Log_a(m/n)=?

Log_a(m)-Log_a(n)

If log_ba= log_bc then…

a = c

Log_aa^x = ?

x

Ln1 = ?

0

Ln(e) = ?

1 (they cancel out)

Ln (e^x) = ?

x

Log (m^A) = ?

A log(m)

Log a^r = ?

r log (a)

Ln a^r = ?

r Ln (a)

Why would you use Ln over log ?

Because only Ln can log e

Log is the same thing as ….?

Ln

Ln is the same thing as ….?

Log

What is a exponential equation?

A exponential equation is an equation in which a varible occurs as a exponent.

(ex: 2e^0.045x )

Ln/ logging cancels out what?

e

e is canceled out b what?

Ln/log

What is the first step when solving a exponential equation?

Isolate the e/ get rid of the the number next to the e.

When rounding a decimal number (x) if the number your rounding with is higher than x what will happen?

x will increase by 1.

When rounding a decimal number (x) if the number your rounding with is lower than x what will happen?

x will stay the same.

When solving an equation that requires you to round always keep the ____ ___ _____.

last two digits.

Solve for x.

15 = 3^2x

x = 1.22

Solve 3.8e^1.5t = 16 algebraically for t to the nearest hundredth

t 0.95

You can or cannot have the answer to an equation with e present

you cannot have the answer to an equation with e present

You can or cannot have the answer to an equation with √ present

can have the answer to an equation with √ present (in certain quadratic equations).

150e^0.05x = 340

x = 16.30

If the equation requires you to round to the nearest thousandth than you need to keep the first ____ digits behind the decimal while solving.

three

If the equation requires you to round to the nearest hundredth than you need to keep the first ____ digits behind the decimal while solving.

two digits

If the equation requires you to round to the nearest tenth than you need to keep the first ____ digits behind the decimal while solving.

1

Solve for the x of 87e^0.3x = 5918, to the nearest thousandth.

14.066