Solve the exponential equation. 0.3^{1+x}=1.7^{2x-1}

varaderiyw

varaderiyw

Answered question

2021-11-20

Solve the exponential equation.
0.31+x=1.72x1

Answer & Explanation

Poul1963

Poul1963

Beginner2021-11-21Added 15 answers

Step 1
We will use the property of logarithms logab=bloga to simplify the given expression. This will be done by taking logarithm on both sides of the equation.
Terms multiplying x will be collected together and constant terms will be moved to the other side of the equation. To solve the equation for x the whole equation will then be divided by the coefficient of x.
Step 2
The given equation is 0.31+x=1.72x1. Take logarithm on both sides and follow the steps mentioned in step 1 to solve for x.
0.31+x=1.72x1
log0.31+x=log1.72x1
(1+x)log0.3=(2x1)log1.7
xlog0.3+log0.3=2xlog1.7log1.7
log0.3+log1.7=2xlog1.7xlog0.3
log0.31.7=x(2log1.7log0.3)
log0.51=x(log1.72log0.3)
log0.51=xlog2.890.3
x=log0.51log2.890.3
Walker Funk

Walker Funk

Beginner2021-11-22Added 13 answers

Calculation:
Obtain the solution of the given exponential equation as follows.
Solve the equation for x as,
0.31+x=1.72x1
ln0.31+x=ln1.72x1 [If M=N, then lnM=lnN]
(1+x)ln0.3=(2x1)ln1.7 [lnMr=rlnM]
ln0.3+xln0.3=2xln1.7ln1.7
Simplify further as,
ln0.3+ln1.7=2xln1.7xln0.3
ln0.3+ln1.7=x(2ln1.7ln0.3)
x=ln0.3+ln1.72ln1.7ln0.3
x0.297
Thus, the solution set for the given exponential equation is {-0.297}.

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