Question

Please Assist. Using Logs to solve Exponential Equations
See Attachment

Answer 1

Do you know how to start?

Answer 2

a^x = b^y
log(a^x) = log(b^y)
x log(a) = y log(b)

Answer 3

log8^T =Log 9^T+1
T Log 8= (T+1)Log 9

Answer 4

yes @Ness9630 but I don't know what to do next

Answer 5

@agent0smith Do you know what to do for this one? I'm drawing a blank at the moment.

Answer 6

starting with
T Log 8= (T+1)Log 9

remember that Log8 and Log9 are just numbers. Distribute the Log9 on the right side
T Log8 = T Log9 + Log9
subtract T Log9 from both sides
T Log8 - T Log9 = Log9
factor out T on the left side
T (Log8 - Log9) = Log9
divide both sides by (Log8 - Log9)
T= Log9/ (Log8 - Log9)

you will need a calculator to find T
or type
Log 9/ (Log 8 - Log 9)=
into google
(it does not matter if we use Log base 10 or natural log)

Answer 7

From T Log 8= (T+1)Log 9

use the distributive property... don't let the log8 and log9 confuse you.

Would you know how to solve it if instead it looked like
8T= 9(T+1)

If you do, then you know how to solve it with log8 and log9 (they are just constants!)