Thank you for visiting Solve the following equation Express your answer as either an integer or a fraction in lowest terms tex 625 left 5 4x 1 right 625. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Sure! Let's solve the equation step-by-step:
The given equation is:
[tex]\[ 625 \times 5^{4x - 1} = 625 \][/tex]
To make things simpler, let's first divide both sides of the equation by 625:
[tex]\[ 5^{4x - 1} = 1 \][/tex]
Now, we need to recognize that [tex]\( 5^0 = 1 \)[/tex]. This means the exponent [tex]\( 4x - 1 \)[/tex] must be equal to 0 to make the equation true. So, we can set up the equation:
[tex]\[ 4x - 1 = 0 \][/tex]
Next, we solve for [tex]\( x \)[/tex] by adding 1 to both sides:
[tex]\[ 4x = 1 \][/tex]
Now, divide both sides by 4 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{1}{4} \][/tex]
So, the solution to the equation is [tex]\( x = \frac{1}{4} \)[/tex].
The given equation is:
[tex]\[ 625 \times 5^{4x - 1} = 625 \][/tex]
To make things simpler, let's first divide both sides of the equation by 625:
[tex]\[ 5^{4x - 1} = 1 \][/tex]
Now, we need to recognize that [tex]\( 5^0 = 1 \)[/tex]. This means the exponent [tex]\( 4x - 1 \)[/tex] must be equal to 0 to make the equation true. So, we can set up the equation:
[tex]\[ 4x - 1 = 0 \][/tex]
Next, we solve for [tex]\( x \)[/tex] by adding 1 to both sides:
[tex]\[ 4x = 1 \][/tex]
Now, divide both sides by 4 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{1}{4} \][/tex]
So, the solution to the equation is [tex]\( x = \frac{1}{4} \)[/tex].
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Rewritten by : Jeany
