Question

can someone help me find x ?

Answer 1

how far did you get?

Answer 2

i started by divine by 2

Answer 3

dividing *

Answer 4

that's a good start

Answer 5

ahemm hint: \(\large {
2(10^{x-5})=24\implies (10^{x-5})=\cfrac{\cancel{24}}{\cancel{2}}\implies
10^{x-5}=12
\\ \quad \\
{\color{brown}{ 10^{x-5}\implies 10^x\cdot 10^{-5} }}\qquad thus
\\ \quad \\
10^x\cdot 10^{-5}=12\implies 10^x\cdot \cfrac{1}{10^5}=12\implies \cfrac{10^x}{10^5}=12
}\)

Answer 6

after doing that, you'll have
\[\Large 10^{x-5} = 12\]

Answer 7

yes

Answer 8

Now apply logs to both sides
\[\Large 10^{x-5} = 12\]
\[\Large \log\left(10^{x-5}\right) = \log\left(12\right)\]

Answer 9

The reason we do this is so we can pull down the exponent
\[\Large (x-5)\log\left(10\right) = \log\left(12\right)\]

Answer 10

now what is `log(10)` equal to?
the base of this log is 10

Answer 11

when you log the left side don't the log and the 10 cancel out?

Answer 12

log(10) = 1

so
\[\Large (x-5)\log\left(10\right) = \log\left(12\right)\]
\[\Large (x-5)*1 = \log\left(12\right)\]
\[\Large x-5 = \log\left(12\right)\]

Answer 13

x= log12+5?

Answer 14

\[\Large x = \log\left(12\right)+5\]
yes

Answer 15

can you check if i did my last two problems correctly?

Answer 16

ok

Answer 17

#34 looks perfect

Answer 18

thank you!!!

Answer 19

so does #35

Answer 20

thanks you so much!!!(:

Answer 21

although, I would leave it as \[\Large \frac{e^{24}}{6}\]

Answer 22

okay :)

Answer 23

if you must do an approximation, then it's approximately equal to 4,414,853,688.34449

Answer 24

alrighty