If logh=35
, what is logh3
? Rewrite using the power rule, then evaluate. Write your answer as a fraction.
To solve for log(h), we need to rewrite the equation using the power rule for logarithms. According to the power rule, log(base a) of b^n is equal to n times log(base a) of b.
So, we can rewrite log(h) as 35 = log(base 3) of h^1.
Now we can use the power rule to rewrite log(h^1) as 1 times log(base 3) of h.
Therefore, log(h) = 1 * log(base 3) of h.
Since log(h) = 35, we can substitute this value into the equation:
35 = 1 * log(base 3) of h.
To solve for log(h3), we can use the power rule again. According to the rule, log(base a) of b^c is equal to c times log(base a) of b.
So, log(h3) can be rewritten as 3 times log(base 3) of h.
Now we need to evaluate log(base 3) of h. Since log(base 3) of h is equal to 35/1, we substitute this value into the equation:
log(h3) = 3 * (35/1).
Therefore, log(h3) = 105/1 = 105.