Mister Exam
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How to use it?
- Equation:
- Equation 3x^2-75=0
- Equation sqrt^4(17x^2-16)=x
- Equation (1/2а-1/3b):(b/2-а/3)
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Equation Sqrt(cos^2x-sin^2x)(tg2x-1)=0
- Express {x} in terms of y where:
- 10*x-1*y=10
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
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Identical expressions
- log one / three (five ^(one +log one 5(x)- one /(three ^(1+log15(x)))))=-1+log15(x)
- logarithm of 1 divide by 3(5 to the power of (1 plus logarithm of 15(x) minus 1 divide by (3 to the power of (1 plus logarithm of 15(x))))) equally minus 1 plus logarithm of 15(x)
- logarithm of one divide by three (five to the power of (one plus logarithm of one 5(x) minus one divide by (three to the power of (1 plus logarithm of 15(x))))) equally minus 1 plus logarithm of 15(x)
- log1/3(5(1+log15(x)-1/(3(1+log15(x)))))=-1+log15(x)
- log1/351+log15x-1/31+log15x=-1+log15x
- log1/35^1+log15x-1/3^1+log15x=-1+log15x
- log1 divide by 3(5^(1+log15(x)-1 divide by (3^(1+log15(x)))))=-1+log15(x)
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Similar expressions
- log1/3(5^(1+log15(x)-1/(3^(1-log15(x)))))=-1+log15(x)
- log1/3(5^(1+log15(x)-1/(3^(1+log15(x)))))=+1+log15(x)
- log1/3(5^(1+log15(x)-1/(3^(1+log15(x)))))=-1-log15(x)
- log1/3(5^(1-log15(x)-1/(3^(1+log15(x)))))=-1+log15(x)
- log1/3(5^(1+log15(x)+1/(3^(1+log15(x)))))=-1+log15(x)
log1/3(5^(1+log15(x)-1/(3^(1+log15(x)))))=-1+log15(x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
log(x) 1
1 + ------- - ------------
log(15) log(x)
1 + -------
log(15)
log(1) 3 log(x)
------*5 = -1 + -------
3 log(15)
$$5^{\left(\frac{\log{\left(x \right)}}{\log{\left(15 \right)}} + 1\right) - \frac{1}{3^{\frac{\log{\left(x \right)}}{\log{\left(15 \right)}} + 1}}} \frac{\log{\left(1 \right)}}{3} = \frac{\log{\left(x \right)}}{\log{\left(15 \right)}} - 1$$
Detail solution
Given the equation
$$5^{\left(\frac{\log{\left(x \right)}}{\log{\left(15 \right)}} + 1\right) - \frac{1}{3^{\frac{\log{\left(x \right)}}{\log{\left(15 \right)}} + 1}}} \frac{\log{\left(1 \right)}}{3} = \frac{\log{\left(x \right)}}{\log{\left(15 \right)}} - 1$$
Transfer the right side of the equation left part with negative sign
$$- \frac{\log{\left(x \right)}}{\log{\left(15 \right)}} = -1$$
Let's divide both parts of the equation by the multiplier of log =-1/log(15)
$$\log{\left(x \right)} = \log{\left(15 \right)}$$
This equation is of the form:
By definition log
then
$$x = e^{- \frac{1}{\left(-1\right) \frac{1}{\log{\left(15 \right)}}}}$$
simplify
$$x = 15$$
$$5^{\left(\frac{\log{\left(x \right)}}{\log{\left(15 \right)}} + 1\right) - \frac{1}{3^{\frac{\log{\left(x \right)}}{\log{\left(15 \right)}} + 1}}} \frac{\log{\left(1 \right)}}{3} = \frac{\log{\left(x \right)}}{\log{\left(15 \right)}} - 1$$
Transfer the right side of the equation left part with negative sign
$$- \frac{\log{\left(x \right)}}{\log{\left(15 \right)}} = -1$$
Let's divide both parts of the equation by the multiplier of log =-1/log(15)
$$\log{\left(x \right)} = \log{\left(15 \right)}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$x = e^{- \frac{1}{\left(-1\right) \frac{1}{\log{\left(15 \right)}}}}$$
simplify
$$x = 15$$