hi what do i do, ik we equate but idk what to do after
#logarithms y12
novel relic
abstract gust
hi what do i do, ik we equate but idk what to do after
So 3 × 2^x = 15 - 2^(x+1)
All u have to notice is that 2^(x+1) = 2 × 2^x
abstract gust
like is that basically saying 3 multiplied 2^x
Yes
abstract gust
No need to re-write that
novel relic
So 3 × 2^x = 15 - 2^(x+1)
All u have to notice is that 2^(x+1) = 2 × 2^x
i don't get the second line
what do i do w the 15 and the 3
abstract gust
i don't get the second line
Its just laws of indicies
Ok to make it easier to visualise let u=2^x
novel relic
ignore the pencil but this is what i've got
if this comes up on my mock i will kms 😭
abstract gust
ignore the pencil but this is what i've got
The log step is the last step
I think i just overcomplicated it
Let u = 2^x
So we're just solving 3u = 15-2u
abstract gust
?
abstract gust
6^x = (3×2)^x not 3 × (2^x)
novel relic
is that not just 6^x
abstract gust
is that not just 6^x
Nope
novel relic
how is that not 6^x
abstract gust
6^x = (3×2)^x not 3 × (2^x)
^
abstract gust
I think ur overcomplicating it
abstract gust
Look
3×2^x = 15 - 2^(x+1)
3×2^x = 15 - 2×2^x
Instead of writing 2^x write u
3u=15-2u
5u=15
u=3
2^x = 3
x = log base 2 of 3
novel relic
where the hell did the other 2 come from
the 2nd line
the second line of ur workings
where did the other 2 come from 😭
abstract gust
2^(x+1) = 2×2^x
abstract gust
Raising something to the power of something is just repeated multiplication right?
So 3^4 is just 3×3×3×3
novel relic
this line baffles me:
i'm still genuinely so confused where the extra 2 from the rhs came from
girl i was meant to start modelling with logs half an hour ago but i'm stuck on this
abstract gust
Ok
2¹ × 2^x by laws of indicies the powers add so it equals 2^(x+1)
Does that make sense
novel relic
yep
abstract gust
Oh ok u got it
novel relic
but here the terms are different
it's 3 and 2
they're not the same so idk what to do
abstract gust
The 3 and the 2 are like coefficients
novel relic
kinda like how u can't do a^2 x b^3
i mean
u can to get a^2b^3
but not like (ab)^5
abstract gust
Multiplication is just repeated addition so if it makes it easier
3×2^x = 2^x + 2^x + 2^x
novel relic
yeah so 2^x times that by 2^x times that by 2^x
wait
why are we
nvm
i'll go w the adding
so that should surely be 6^x???
abstract gust
Adding not multiplying
novel relic
this is so fucking confusing bro i'm literally crying
yeah that's still the same inni??
novel relic
if i were to multiply instead that would just be 8x^3
abstract gust
Not x times x times x
abstract gust
if i were to multiply instead that would just be 8x^3
Wait what?
novel relic
where did the extra 2 come from
novel relic
U can solve the equation 3x=15-2x right?
yeah
i'm just like
where did the extra 2 come from
2x2^x is just 4^x
abstract gust
I thought u said u understood that...
novel relic
i understand the other bits after i just don't get that
abstract gust
The base stays the same
abstract gust
Like gcse laws of indicies
novel relic
so 2^1 * 2^x
abstract gust
Yesss
novel relic
that's just 2^x+1
abstract gust
Yessss
novel relic
what am i gonna take from there?? 😭
abstract gust
Then u just rearrange to make 2^x the subject
abstract gust
What cancels out?
abstract gust
I swear if ur trolling
novel relic
so we have to assign some sort of variable to it
i swear i'm not
i'm literally crying in a classroom over this question
abstract gust
Oh ok
abstract gust
so we have to assign some sort of variable to it
That can make it easier
Like u=2^x
novel relic
holy shit why is the quality so bad
abstract gust
Oh damn
novel relic
i was meant to learn exponentials almost an hour ago but i'm stuck on this
like wtf happens to it
i'm just gonna pray this question doesn't come up on the mock
abstract gust
?
regal forge
$a * b^x + c * b^x = (a+c)b^x$
mystic hullBOT
riad
regal forge
The star is multiplication
mystic hullBOT
clarence cant solve d1s
abstract gust
$a\times b$
$a×b$
mystic hullBOT
arizus
abstract gust
🧠🧠