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chwala
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- Homework Statement
- let ##x,y,z>1##, and ##m>1## so that ##log_{xy}m=9##
##log_{yz}m=18##
##log_{xyz}m=8##
find ##log_{xz}m##
- Relevant Equations
- logarithms
this is my working...
chwala said:Homework Statement:: let ##x,y,z>1##, and ##m>1## so that ##log_{xy}m=9##
##log_{yz}m=18##
##log_{xyz}m=8##
find ##log_{xz}##
Relevant Equations:: logarithms
View attachment 265398
this is my working...
The problem statement is incomplete. ##\log_{xy}## of what?find ##log_{xz}##
You can transform this into a set of linear equations:chwala said:find ##log_{xz}m##...i checked with my colleague, my solution is correct, i would be looking at probably an alternative approach. thanks
PeroK said:You can transform this into a set of linear equations:
$$9x + 9y = 1, \ \ \ 18y + 18z = 1, \ \ \ 8x + 8y + 8z = 1$$
And you want to find ##a## such that:
$$ax + az = 1$$
A logarithm is the inverse operation of exponentiation. It helps us solve problems involving exponential growth or decay.
To solve a logarithm problem, you need to use the properties of logarithms and algebraic manipulation. Start by rewriting the logarithmic equation in exponential form, then use the properties of logarithms to simplify the equation. Finally, solve for the unknown variable.
The three main properties of logarithms are:
Some common mistakes when solving logarithm problems include:
While a calculator can be helpful, it is not always necessary to solve logarithm problems. With the proper understanding of logarithms and their properties, you can solve many logarithm problems without a calculator. However, for more complex problems, a calculator may be useful.