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Need help with logarithmic?
1) If log(x+1)^27=3, what is he value of x?
2) If log 2=a and log3=b, express log square root of 6 in terms a and b
Please show the steps and explain to me how to solve this. Thanks.
2 Answers
- mecdubLv 71 decade agoFavorite Answer
1. log (x + 1)^27 = 3
27 log (x + 1) = 3
log (x + 1) = 3/27 = 1/9
x + 1 = 10^(1/9)
x = 10^(1/9) - 1
2. log √6
= log (√3 * √2)
= log √3 + log √2
= ½ log 3 + ½ log 2
= ½(log 3 + log 2)
= ½(a + b)
- billrussell42Lv 71 decade ago
log(x+1)^27 = 3
both sides to power of 10
(x+1)^27 = 1000
x+1 = 1000^(1/27)
x = 1000^(1/27) – 1
x = 0.2915493
√6 = x
x = √3√2
log both sides
log x = log√2 + log√3
log x = (1/2) log2 + (1/2) log3
log x = (1/2) a + (1/2) b
log x = (1/2) (a + b)
raise both sides to power of 10
x = 10^(a/2 + b/2)
.
