Log6(6^9)=???
Answer: 9
Ine^-3x=???
Answer: -3x
Use log5(2) = 0.4307 and log5(3) = 0.6826 to approximate the value of log5(12)
Answer:
log5(2) + log5(3)=log5(2^2*3)
2(0.4307) + 0.6826=1.544
so approximate value of log5(12)=1.544
I appreciate your checking my work.
Log6(6^9)=???
9 log6(6) = 9*1
Answer: 9 Right
Ine^-3x=???
Answer: -3x Right
Use log5(2) = 0.4307 and log5(3) = 0.6826 to approximate the value of log5(12)
Answer:
log5(***4***) + log5(3)=log5(2^2*3)
2(0.4307) + 0.6826=1.544
Right method,, did not check arithmetic
so approximate value of log5(12)=1.544
To find the value of log6(6^9), we can use the logarithmic property that log base b of b^x is equal to x. Therefore, the value of log6(6^9) is simply 9.
Now let's solve the equation ine^-3x. We can rewrite this equation as e^-3x = i. To isolate x, we take the natural logarithm (ln) of both sides: ln(e^-3x) = ln(i). The ln and e functions are inverses, so the e and ln cancel out on the left side, leaving -3x = ln(i). Since ln(i) equals the imaginary unit i times pi/2 (i * pi/2), the equation becomes -3x = i * pi/2. Thus, the answer is -3x.
To approximate the value of log5(12), we can use the logarithmic property that log base b of (mn) is equal to log base b of m plus log base b of n. Using the given values log5(2) = 0.4307 and log5(3) = 0.6826, we can calculate log5(12) as follows:
log5(12) = log5(2^2 * 3)
= log5(2^2) + log5(3)
= 2 * log5(2) + log5(3)
= 2 * 0.4307 + 0.6826
= 0.8614 + 0.6826
= 1.544
Therefore, the approximate value of log5(12) is 1.544.
I'm glad to check your work and provide explanations. If you have any more questions, feel free to ask!