Logarithm Questions (1 Viewer)

[Menomaths]

Hey guys, doing the Logarithm section now so might be posting a few questions later on ^.^
1) 10^log10 3 (10 to the power log(base 10) 3 -my working; Actually got the correct answer but not sure if it's a legitimate working or just luck.
10^log10 3
log10 3 = x
10^x = 3
Therefore answer is 3, since log10 3 = x and 10^x = 3 so substituting in 10^log10 3 gives 3

2) log10 125+ log10 25+ log10 5 - my working; log10 (125*25*5) = log10(15625) Gave up here.
Sorry I can't use Latex, that's because my shift, b and a few other keys don't work. Have to use copy paste for all my b's and on-screen keyboard for other keys.

 

[braintic]

The first one you should just know - a^[log_a (x)] = x. The exponential undoes the log.

log_10 (5^6) = log_10 (10^6 / 2^6) = log_10 (10^6) - log_10 (2^6) = 6 - 6*log_10 (2)

 

[Menomaths]

The first one you should just know - a^[log_a (x)] = x. The exponential undoes the log.

log_10 (5^6) = log_10 (10^6 / 2^6) = log_10 (10^6) - log_10 (2^6) = 6 - 6*log_10 (2)

The answer for the second one is 3

 

[Menomaths]

NOOOOOOOOOOOOOOOOOOOOO I've been looking at the wrong answer the whole time fml

 

[Menomaths]

This one I didn't mix the answers up;
2log x+3 = log x^5
Thanks in advance
*all logs are base 10

 

[lochnessmonsta]

3 = log x^5 -log x^2
3 = log x^3
x^3 = 10^3
x = 10

 

[cineti970128]

2) note that 5^3 = 125
5^2 = 25
hence log(125) + log(25) + log(5) = 6log 5

 

[Menomaths]

3 = log x^5 -log x^2
3 = log x^3
x^3 = 10^3
x = 10

Ah thanks

 

[Menomaths]

Find the value of x for which
(logx)(logx^2) + logx^3 -5 = 0
They're all base 10