Question

how do i solve this? 7^2t-1=35

Answer 1

do you mean
\[ \Large 7^{2t}-1=35 \]

Answer 2

no it's 2t-l in the exponent

Answer 3

\[7^{2t-1} = 35\] huh

Answer 4

you take the log

Answer 5

\[\log_7 35 = 2t - 1\]

Answer 6

\[\log_7 35 + 1 = 2t\]

Answer 7

\[\frac{\log_7 35 + 1}{2} = t\]

Answer 8

using my notes, im supposed to solve it this way 2t log7-log7=log35

Answer 9

oh i see...that's possible...do you want to know where it came from?

Answer 10

i know how to get to that point but dont know where to go from there

Answer 11

take the log of both sides
\[(2t-1)\log 7 = \log 35\]
distribute
\[2t\log 7 - \log 7 = \log 35\]
\[2t \log 7 = \log 35 + \log 7\]
\[2t = \frac{\log(35 \times 7)}{\log 7}\]
\[t = \frac{\log (35\times 7)}{2\log 7}\]

Answer 12

hah lol

Answer 13

\[t = \frac{\log 245}{2\log 7}\]
\[t = \frac 12 \frac{\log 245}{\log 7}\]
\[t = \frac 12 \log_7 245\]

Answer 14

\[t = \log_7 \sqrt{245}\]

Answer 15

im not sure if that's same as what i initially wrote though

Answer 16

the final rounded answer should come to 1.41 i just have no idea how to get to that

Answer 17

if you have a calculator just type if what @lgbasallote wrote first
\[ \Large t=\frac{\log 245}{2\log 7}=1.413543... \]