Question

Find the value of x in each of the following equations. @ganeshie8

Answer 1

\[6^{2x+1}=5^{x}\]

Answer 2

\[2x+1=\log _{6}5^x\]

Answer 3

yes that corrrect

Answer 4

Next step what should we do?

Answer 5

@AlexandervonHumboldt2

Answer 6

HI!!

Answer 7

if you actually want an answer, you cannot do it this way
you have to rewrite it in terms of either log base ten, or the natural log

Answer 8

\[6^{2x+1}=5^x\\
(2x+1)\ln(x)=x\ln(5)\] then algebra

Answer 9

oops typo

Answer 10

\[6^{2x+1}=5^x\\
(2x+1)\ln(6)=x\ln(5)\]

Answer 11

damn typos!!

Answer 12

third time is a charm

Answer 13

solve that equation for \(x\) using algebra
remember that \(\ln(6)\) and \(\ln(5)\) are just numbers

Answer 14

can u show me the working? @misty1212

Answer 15

yeah it is all algebra

Answer 16

\[(2x+1)\ln(6)=x\ln(5)\] distribute
\[2\ln(x)x+\ln(6)=x\ln(5)\]

Answer 17

subtract \(2\ln(6)\ln(x)\) from both sides
\[\ln(6)=x\ln(5)-2\ln(6)x\]

Answer 18

factor out the \(x\)
\[\ln(6)=x(\ln(5)-2\ln(6))\]

Answer 19

then divide to solve for \(x\)

Answer 20

Thnx @misty1212

Answer 21

Answer will be
x=-0.9076

Answer 22

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