Another another more challenging log question.

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The discussion revolves around solving the logarithmic equation log6(5y − 5) = 4x^2 + 7. Participants emphasize the importance of rewriting the logarithmic equation in its exponential form, which is crucial for solving it correctly. There is confusion regarding the attempted solution, as it does not maintain the proper equation format or follow the necessary steps for transformation. The suggestion is made to isolate one variable and substitute it back into the original equation for a clearer solution pathway. Overall, the focus is on ensuring the correct application of logarithmic and exponential properties in solving the equation.
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another another more challenging log question. :(

Homework Statement


log6(5y − 5) = 4x^2 + 7


Homework Equations



-

The Attempt at a Solution


6( x^2 + 6x+5 ) +1
 
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hibachii said:

Homework Statement


log6(5y − 5) = 4x^2 + 7


Homework Equations



-

The Attempt at a Solution


6( x^2 + 6x+5 ) +1

You started with an equation - you should end with an equation.

An equation of the form logb(M) = N can be rewritten as an exponential equation of the form M = bN.
 


isnt that what i did (given in the attempted solution)?
 


No. For one thing, what you wrote isn't an equation, and it should be. For another thing, what you wrote doesn't follow the same pattern as the exponential equation I wrote.
 


hibachii said:

Homework Statement


log6(5y − 5) = 4x^2 + 7


Homework Equations



-

The Attempt at a Solution


6( x^2 + 6x+5 ) +1

64x^2+7=5y-5
Take the log of both sides now.
log64x^2+7=log5y-5
(4x2+7)log6=log5y-5

From here, isolate for one of the variables and substitute it into the original equation. Solve for the other once that is done.
 


What is your question?
Taking the exponential of both sides and then the log again really defeats the purpose of getting anywhere...
 

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