Question

How to solve an exponential equation? 5^(x+6)=7

Answer 1

I know I have to take the log of both sides.

Answer 2

\[log_5(7) = (x+6)\]

Answer 3

I'm confused. where did the 5 with the x+6 go?

Answer 4

To use a calculator with common log of base-10, do log(7) divided by log(base). in this case \[\frac{log7}{log5}\]

Answer 5

\[log_5(some number)\] is asking, what power of 5 is equal to somenumber

Answer 6

ok

Answer 7

so \[\frac{log7}{log5} = x+6\] and solve for x

Answer 8

thank you!

Answer 9

yw :)

Answer 10

could you help me with one more problem?

Answer 11

Just be sure to remember that trick. Sometimes we have to change our log base, and a lot of calculators don't have an easily accessible button for this. TI calcs may have it buried in their menu systems but I never bother cause it takes too long.

Answer 12

sure, if i am able to

Answer 13

ok. \[\log_{8}(x^2-7x) = 1 \]

Answer 14

This is saying 8 raised to the power 1 is equal to x^2-7x.

Answer 15

so quadratic formula?

Answer 16

\[log_{10}(100) = ?\]

Answer 17

Not related, but solve it.

Answer 18

?=2

Answer 19

Right.

Answer 20

So the little base number is always raised to the power on the right side of the equal, and the answer is inside the ( ).

Answer 21

Just remember that.

Answer 22

ok

Answer 23

\[x^2-7x = 8^1\]

Answer 24

\[x^2 - 7x - 8 = 0\]

Answer 25

factor and solve for x, setting each term equal to zero

Answer 26

\[x^2-7x-8 = (x-8)(x+1)\]

Answer 27

set each term equal to zero and solve for x.

To factor \[x^2-7x-8\] i found two numbers that multiply to get -8 and add to get -7

Answer 28

you could use quadractic equation but that is slower

Answer 29

right

Answer 30

\[[(x-8)=0 ]\wedge [(x+1) = 0]\]

Answer 31

x = 8 and x = -1

Answer 32

\ok. that makes much more sense than when my teacher explained it

Answer 33

\[\wedge\] is a symbol for and

Answer 34

cool :) that's what OS is for

Answer 35

wait till you get to calclulus, then you start enjoying math cause it's useful and not boring lol. but u gotta master algebra 1st so you're doing good

Answer 36

haha. this is calculus, at least, that's what the class is called

Answer 37

pre-calculus?

Answer 38

yea, sorry. pre-calc

Answer 39

almost there!

Answer 40

not taking calculus next year at all.

Answer 41

no, my teacher made it clear that if we don't get this then we should just work at McD's/ so thats what im doing.

Answer 42

oh man you should that's where everything starts to get interesting

Answer 43

it's true

Answer 44

(minimum wage waste-of-life jobs without advanced analytical skills)

Answer 45

alright message anytime. best wishes, good job :)

Answer 46

thank u!