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If log_a(16) = 4, what is the value of a? (2021)
If log_a(16) = 4, what is the value of a? (2021)
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Q1
If log_a(16) = 4, what is the value of a? (2021)
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16
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log_a(16) = 4 implies a^4 = 16. Since 16 = 2^4, we have a^4 = 2^4, thus a = 2.
Questions & Step-by-step Solutions
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Q
Q: If log_a(16) = 4, what is the value of a? (2021)
Solution:
log_a(16) = 4 implies a^4 = 16. Since 16 = 2^4, we have a^4 = 2^4, thus a = 2.
Steps: 5
Show Steps
Step 1: Start with the equation log_a(16) = 4.
Step 2: Understand that log_a(16) = 4 means that a raised to the power of 4 equals 16.
Step 3: Rewrite the equation as a^4 = 16.
Step 4: Recognize that 16 can be expressed as 2 raised to the power of 4, so rewrite it: a^4 = 2^4.
Step 5: Since both sides of the equation have the same exponent (4), we can set the bases equal to each other: a = 2.
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