Solve for t using logarithms with base a. Please help.

Question

zappy620 · Answer

$$2a ^{t/3}=5$$

anonymous · Answer

2a^t/3=5 

a^t/3=(5/2) ; and take log(base a) 
log(base a) a^t/3 = log(base a)(5/2) 

t/3 = log(base a)(5/2) 
t = 3log(base a)(5/2) ANS...

anonymous · Answer

am i tight @satellite73

zappy620 · Answer

u factored out a?

anonymous · Answer

right

anonymous · Answer

you looking for a number, as in a decimal?

zappy620 · Answer

not a decimal

anonymous · Answer

does your answer have a $\log_a(~)$ in it?

zappy620 · Answer

yes

anonymous · Answer

the go with what @hockeybeast10  said

anonymous · Answer

2a^t / 3 = 5 

Multiply both sides by 3. 

2a^t = 15 

Divide both sides by 2. 

a^t = (15/2) 

Here's where you convert this into logarithmic form. Remember that 

b^c = x in logarithmic form is log[base b](x) = c. 

log[base a](15/2) = t

zappy620 · Answer

but 3 is in the exponent, can you still do that?

anonymous · Answer

hmmm... would it be like this then?
2a^(t/3) = 5 
a^(t/3) = 2.5 
log(a^(t/3) = log(2.5) 
(t/3) log a = log(2.5) 
t/3 = log(2.5) 
t = 3.log 5

zappy620 · Answer

yea however i left it in fractions let me try it real quick

anonymous · Answer

okay

anonymous · Answer

yes it would be like the second one, except you made a typo in the last step

anonymous · Answer

$$\frac{t}{3}=\log_a(2.5)\
t=3\log_a(2.5)$$

anonymous · Answer

ohhhhh i see it:0 sorry

anonymous · Answer

@zappy620 are you good? do you need anything els?

zappy620 · Answer

I just got it thank you so much :D

anonymous · Answer

np