How to Solve Logarithmic Equations with Different Bases?

emma3001 · Jun 11, 2008

Solve the equation log2x + log4x= 5. To start, should I change this to an exponential... I am stuck because I have only done log questions that have the same base.

Dick · Jun 11, 2008

Convert them to the same base log_a(x)=log_b(x)/log_b(a).

HallsofIvy · Jun 12, 2008

emma3001 said:

Solve the equation log2x + log4x= 5. To start, should I change this to an exponential... I am stuck because I have only done log questions that have the same base.

What do you mean by "log2x+ log4x= 5"? I would interpret that as log(2x)+ log(4x)= 5 so log(6x)= 5 which is easy. If you mean "log_2(x)+ log_4(x)= 5" then use Dick's hint.
log_4(x)= log_2(x)/log_2(4)= ?

kim1214 · Aug 19, 2008

Dick said:

Convert them to the same base log_a(x)=log_b(x)/log_b(a).

can u help solving a problem?

kim1214 · Aug 19, 2008

can u help solve a problem?

Dick · Aug 19, 2008

Can u post the problem? Under Forum Tools, "Post a New Thread". That's your first step.

How to Solve Logarithmic Equations with Different Bases?

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