Question
Solve the equation
Solve for x
x1=−56,x2=514
Alternative Form
x1=−1.2,x2=2.8
Evaluate
log10(∣4−5x∣)×2=2
Find the domain
More Steps
Evaluate
∣4−5x∣>0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x,except when ∣4−5x∣=0
∣4−5x∣=0
Rewrite the expression
4−5x=0
Move the constant to the right-hand side and change its sign
−5x=0−4
Removing 0 doesn't change the value,so remove it from the expression
−5x=−4
Change the signs on both sides of the equation
5x=4
Divide both sides
55x=54
Divide the numbers
x=54
Exclude the impossible values of x
x=54
log10(∣4−5x∣)×2=2,x=54
Multiply the terms
2log10(∣4−5x∣)=2
Divide both sides
22log10(∣4−5x∣)=22
Divide the numbers
log10(∣4−5x∣)=22
Divide the numbers
More Steps
Evaluate
22
Reduce the numbers
11
Calculate
1
log10(∣4−5x∣)=1
Convert the logarithm into exponential form using the fact that logax=b is equal to x=ab
∣4−5x∣=101
Evaluate the power
∣4−5x∣=10
Separate the equation into 2 possible cases
4−5x=104−5x=−10
Solve the equation for x
More Steps
Evaluate
4−5x=10
Move the constant to the right-hand side and change its sign
−5x=10−4
Subtract the numbers
−5x=6
Change the signs on both sides of the equation
5x=−6
Divide both sides
55x=5−6
Divide the numbers
x=5−6
Use b−a=−ba=−ba to rewrite the fraction
x=−56
x=−564−5x=−10
Solve the equation for x
More Steps
Evaluate
4−5x=−10
Move the constant to the right-hand side and change its sign
−5x=−10−4
Subtract the numbers
−5x=−14
Change the signs on both sides of the equation
5x=14
Divide both sides
55x=514
Divide the numbers
x=514
x=−56x=514
Check if the solution is in the defined range
x=−56x=514,x=54
Find the intersection of the solution and the defined range
x=−56x=514
Solution
x1=−56,x2=514
Alternative Form
x1=−1.2,x2=2.8
Show Solution