Expand the logarithmic expression.
log8 a/2
My answer is log8a-log8 2
Your answer is correct, the multiple choice answers are
1. C
2. D
3. A
4. A
5. D
6. B
7. A
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Thank you Lola! For the second half, here are the answers;
1.
5e^2x + 11 = 30
Divide the 5
e^2x + 11 = 6
Apply log rules
2x + 11 = ln(6)
Isolate the x
x = (ln(6)-11)/2
or
x=-4.604...
2.
ln(5x + 7) = 8
Apply log rules
5x + 7 = e^8
Isolate x
x = (e^8 - 7)/5
or
x = 594.792...
3.
log 8x^3 = 4
Assuming log base is 10
log_10 8x^3 = 10^4
Cancel out the log
8x^3 = 10000
Isolate the x
x^3 = 1250
Simplify
x = 10.772
4.
1/16 = 64^(4x-3)
Apply exponent rules
-2 = 3(4x-3)
isolate x
x = 7/12
or
x = 0.583
5.
log_3 40 - log_3 10
Apply log rules
log_3 (40/10)
Divide
log_3 4
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Thank you lola.
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It's always nice to get correct answers.
but log8 2 = 1/3
so
log8 (a/2)
= log8 a - 1/3