QuestionExpress $10^{0.3010}=2$ in logarithm form

Studdy Solution

STEP 1

1. The given expression $10^{0.3010}=2$ involves an exponent with a base of 10.
2. To convert this expression into logarithmic form, we will use the properties of logarithms, specifically the relationship between exponential and logarithmic forms.

STEP 2

1. Understand the relationship between exponential and logarithmic forms.
2. Rewrite the given exponential equation in its equivalent logarithmic form.

STEP 3

Recall the general relationship between exponential and logarithmic forms. If $a^b = c$ , then $\log_a(c) = b$ . Here, $a$ is the base, $b$ is the exponent, and $c$ is the result.
$a^b = c \implies \log_a(c) = b$

STEP 4

Identify the corresponding parts of the given equation $10^{0.3010}=2$ to fit into the logarithmic form $\log_a(c) = b$ . Here, the base $a$ is 10, the exponent $b$ is 0.3010, and the result $c$ is 2.
$10^{0.3010} = 2 \implies \log_{10}(2) = 0.3010$
Solution: The given expression $10^{0.3010}=2$ in logarithmic form is:
$\log_{10}(2) = 0.3010$

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