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If a^x = b^y, then log_a(b) is equal to?
If a^x = b^y, then log_a(b) is equal to?
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Practice Questions
1 question
Q1
If a^x = b^y, then log_a(b) is equal to?
y/x
x/y
x+y
y-x
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From a^x = b^y, taking log_a on both sides gives log_a(b^y) = x, hence y * log_a(b) = x, thus log_a(b) = y/x.
Questions & Step-by-step Solutions
1 item
Q
Q: If a^x = b^y, then log_a(b) is equal to?
Solution:
From a^x = b^y, taking log_a on both sides gives log_a(b^y) = x, hence y * log_a(b) = x, thus log_a(b) = y/x.
Steps: 5
Show Steps
Step 1: Start with the equation a^x = b^y.
Step 2: Take the logarithm base a of both sides of the equation. This gives us log_a(a^x) = log_a(b^y).
Step 3: Use the property of logarithms that states log_a(a^x) = x. So, we have x = log_a(b^y).
Step 4: Apply the power rule of logarithms, which states log_a(b^y) = y * log_a(b). Now we have x = y * log_a(b).
Step 5: To find log_a(b), rearrange the equation: log_a(b) = x / y.
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