diff --git a/doc/modules/model_evaluation.rst b/doc/modules/model_evaluation.rst
index eeb058e1440c1..e55dc1cc14762 100644
--- a/doc/modules/model_evaluation.rst
+++ b/doc/modules/model_evaluation.rst
@@ -176,7 +176,7 @@ Here is an example of building custom scorers, and of using the
     >>> import numpy as np
     >>> def my_custom_loss_func(y_true, y_pred):
     ...     diff = np.abs(y_true - y_pred).max()
-    ...     return np.log(1 + diff)
+    ...     return np.log1p(diff)
     ...
     >>> # score will negate the return value of my_custom_loss_func,
     >>> # which will be np.log(2), 0.693, given the values for X
diff --git a/examples/plot_isotonic_regression.py b/examples/plot_isotonic_regression.py
index fd076b5afad62..2411aa1d95124 100644
--- a/examples/plot_isotonic_regression.py
+++ b/examples/plot_isotonic_regression.py
@@ -28,7 +28,7 @@
 n = 100
 x = np.arange(n)
 rs = check_random_state(0)
-y = rs.randint(-50, 50, size=(n,)) + 50. * np.log(1 + np.arange(n))
+y = rs.randint(-50, 50, size=(n,)) + 50. * np.log1p(np.arange(n))
 
 # #############################################################################
 # Fit IsotonicRegression and LinearRegression models
diff --git a/sklearn/gaussian_process/gpc.py b/sklearn/gaussian_process/gpc.py
index e1f37617b6d1e..51da24fccc77b 100644
--- a/sklearn/gaussian_process/gpc.py
+++ b/sklearn/gaussian_process/gpc.py
@@ -409,7 +409,7 @@ def _posterior_mode(self, K, return_temporaries=False):
             # Line 10: Compute log marginal likelihood in loop and use as
             #          convergence criterion
             lml = -0.5 * a.T.dot(f) \
-                - np.log(1 + np.exp(-(self.y_train_ * 2 - 1) * f)).sum() \
+                - np.log1p(np.exp(-(self.y_train_ * 2 - 1) * f)).sum() \
                 - np.log(np.diag(L)).sum()
             # Check if we have converged (log marginal likelihood does
             # not decrease)
diff --git a/sklearn/metrics/regression.py b/sklearn/metrics/regression.py
index 4bc88561a73fd..e9084a4276e18 100644
--- a/sklearn/metrics/regression.py
+++ b/sklearn/metrics/regression.py
@@ -314,7 +314,7 @@ def mean_squared_log_error(y_true, y_pred,
         raise ValueError("Mean Squared Logarithmic Error cannot be used when "
                          "targets contain negative values.")
 
-    return mean_squared_error(np.log(y_true + 1), np.log(y_pred + 1),
+    return mean_squared_error(np.log1p(y_true), np.log1p(y_pred),
                               sample_weight, multioutput)
 
 
diff --git a/sklearn/neighbors/binary_tree.pxi b/sklearn/neighbors/binary_tree.pxi
index 6b736d39fab82..3e17f1b93d6c0 100755
--- a/sklearn/neighbors/binary_tree.pxi
+++ b/sklearn/neighbors/binary_tree.pxi
@@ -486,7 +486,7 @@ cdef DTYPE_t _log_kernel_norm(DTYPE_t h, ITYPE_t d,
     elif kernel == EXPONENTIAL_KERNEL:
         factor = logSn(d - 1) + lgamma(d)
     elif kernel == LINEAR_KERNEL:
-        factor = logVn(d) - log(d + 1.)
+        factor = logVn(d) - np.log1p(d)
     elif kernel == COSINE_KERNEL:
         # this is derived from a chain rule integration
         factor = 0
diff --git a/sklearn/utils/_logistic_sigmoid.pyx b/sklearn/utils/_logistic_sigmoid.pyx
index 58809eb7c1b7b..9c7b8d0a20843 100644
--- a/sklearn/utils/_logistic_sigmoid.pyx
+++ b/sklearn/utils/_logistic_sigmoid.pyx
@@ -13,9 +13,9 @@ ctypedef np.float64_t DTYPE_t
 cdef DTYPE_t _inner_log_logistic_sigmoid(DTYPE_t x):
     """Log of the logistic sigmoid function log(1 / (1 + e ** -x))"""
     if x > 0:
-        return -log(1 + exp(-x))
+        return -np.log1p(exp(-x))
     else:
-        return x - log(1 + exp(x))
+        return x - np.log1p(exp(x))
 
 
 def _log_logistic_sigmoid(int n_samples, int n_features,